This article is part of a series about our increasing understanding of the meanings behind the designs of Anglo-Saxon art. For other chapters click here.
Secrets in the Stones: Decoding Anglo-Saxon Art. Part 4
Secrets in the Stones: Decoding Anglo-Saxon Art. Part 4
The Garnet Code
Early Anglo-Saxon jewellery is renowned for its use of gold and garnet work. Until now, the significance of garnets as a material has not been thoroughly investigated. In this article, and a public lecture at Soulton Hall, Shropshire (delivered simultaneously with this article’s timed release) James D. Wenn draws together the geometry of the garnet crystal with the geometry within Anglo-Saxon art and architecture, signposting to the previous articles in this series. This is then coupled with later examples of this geometry, notably the Cosmati Pavement in Westminster Abbey, to link the philosophical meaning of this geometry to Plato’s book ‘Timaeus’, and both pre-Christian and Christian cosmology and theology.
Early Anglo-Saxon jewellery is renowned for its use of gold and garnet work. Until now, the significance of garnets as a material has not been thoroughly investigated. In this article, and a public lecture at Soulton Hall, Shropshire (delivered simultaneously with this article’s timed release) James D. Wenn draws together the geometry of the garnet crystal with the geometry within Anglo-Saxon art and architecture, signposting to the previous articles in this series. This is then coupled with later examples of this geometry, notably the Cosmati Pavement in Westminster Abbey, to link the philosophical meaning of this geometry to Plato’s book ‘Timaeus’, and both pre-Christian and Christian cosmology and theology.
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Copyright and citations notice
The synthesis between observations made in this article is the intellectual property of James D. Wenn and Byrga Geniht Ltd. The form of words is copyright James D. Wenn and Byrga Geniht Ltd, 2023. Pictures, diagrams and links remain property of their respective copyright holders. Licences may be sought for use of Byrga Geniht Ltd images and text by contacting Byrga Geniht Ltd. Thegns of Mercia hold a permanent licence for use of Byrga Geniht Ltd text and images within this article. Thegns of Mercia is the publisher of this article. Citations of this article must reference James D. Wenn and Thegns of Mercia, and link to this article or reproduce its URL. |
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Author
James D. Wenn holds an MA in Anglo-Saxon, Norse and Celtic from the University of Cambridge, and an MA in The English Country House from Leicester University. He is a trustee of the Essex Cultural Diversity Project, and founder of Byrga Geniht consultancy. He has been a member of the Thegns since 2019.
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Introducing the Garnet
Garnets are silicate minerals whose habit is cubic or rhombic-dodecahedral. The garnets that are seen in early Anglo-Saxon jewellery have been laboriously polished down to form shiny pieces of gemstone that fit together into cloisonne-like mosaic work, or stand alone as cabochon (domed) specimens fixed by bezels (arcs of metal that grip the edges of the stone). This tendency to work the garnet stones means that the natural form of the garnet crystal is unfamiliar to many people who are otherwise familiar with Anglo-Saxon lapidary work.
A rhombic dodecahedron has twelves faces, each of which is an identical rhombus ‒ a lozenge with straight edges of equal length, whose opposite corners have the same angles.
The natural rhombic-dodecahedral form of the garnet is shown in the attached photograph of the author at a Thegns of Mercia event at Sutton Hoo in 2022. The specimen shown was mined in Africa, but we know that the garnets used in the Sutton Hoo and Staffordshire Hoard jewellery derived from central Europe and India.
The linked video shows how a rhombic dodecahedron can be made out of two cubes. If you pull apart one of the cubes by its six square faces, you find each face carries with it a pyramid of material that narrows into the centre. In other words, you can make a cube out of six identical square-based pyramids.
The natural rhombic-dodecahedral form of the garnet is shown in the attached photograph of the author at a Thegns of Mercia event at Sutton Hoo in 2022. The specimen shown was mined in Africa, but we know that the garnets used in the Sutton Hoo and Staffordshire Hoard jewellery derived from central Europe and India.
The linked video shows how a rhombic dodecahedron can be made out of two cubes. If you pull apart one of the cubes by its six square faces, you find each face carries with it a pyramid of material that narrows into the centre. In other words, you can make a cube out of six identical square-based pyramids.
Place the square bases of these six pyramids onto the square faces of the other, identical, cube. Each of the 24 triangular faces of the pyramids will now align with a partner, turning the pair into a single rhombus. These new shapes make the solid’s 12 faces.
The ratio of each face is a width of value one, to a length of the square root of two. A way to intuit why this ratio includes the square root of two takes us back to the ‘pyramid method’ of constructing a rhombic dodecahedron. Let each edge of the initial cubes measure 1. The edges of the pyramids around the square base therefore also measure 1. The apex of each pyramid was once the centre of the cube. So, if we take a line from the middle of an edge of the original cube to the centre, this is the same as taking a line from the apex to the middle of the edge at the base of a pyramid. If we extend this line through the cube past the centre to the middle of the opposite edge of the cube, this is the same as the length of one of the rhombuses/lozenges on the rhombic dodecahedron. A cross section of the cube would be a square with a diagonal corner-to-corner line, making two identical right-angled triangles. As each triangle is right-angled, we can apply Pythagoras’ Theorem — the first short edge squared, plus the second short edge squared, equals the long edge (the hypotenuse) squared — as follows: (1x1)+(1x1)=2. The hypotenuse thus measures the square root of 2, and so does the route through the cube, and the length of the rhombus in the rhombic dodecahedron.
Now imagine we have a stack of cubes, with all their faces and edges lined up. Take one cube within the stack, and divide it into six pyramids (without moving anything). Attach each of these pyramids to the cube whose square face touches it. Then take these new solids, and similarly divide-then-attach the five other cubes that touch each of them, so that they also become rhombic dodecahedra. Repeat the process. This should make it clear how identical rhombic dodecahedra can be used to fill a three-dimensional volume without gaps. It may help to think of this like a 3D chess board where each dark cube is the core of a rhombic dodecahedron, and each white cube provides one pyramid to each adjoining dark cube.
The ratio of each face is a width of value one, to a length of the square root of two. A way to intuit why this ratio includes the square root of two takes us back to the ‘pyramid method’ of constructing a rhombic dodecahedron. Let each edge of the initial cubes measure 1. The edges of the pyramids around the square base therefore also measure 1. The apex of each pyramid was once the centre of the cube. So, if we take a line from the middle of an edge of the original cube to the centre, this is the same as taking a line from the apex to the middle of the edge at the base of a pyramid. If we extend this line through the cube past the centre to the middle of the opposite edge of the cube, this is the same as the length of one of the rhombuses/lozenges on the rhombic dodecahedron. A cross section of the cube would be a square with a diagonal corner-to-corner line, making two identical right-angled triangles. As each triangle is right-angled, we can apply Pythagoras’ Theorem — the first short edge squared, plus the second short edge squared, equals the long edge (the hypotenuse) squared — as follows: (1x1)+(1x1)=2. The hypotenuse thus measures the square root of 2, and so does the route through the cube, and the length of the rhombus in the rhombic dodecahedron.
Now imagine we have a stack of cubes, with all their faces and edges lined up. Take one cube within the stack, and divide it into six pyramids (without moving anything). Attach each of these pyramids to the cube whose square face touches it. Then take these new solids, and similarly divide-then-attach the five other cubes that touch each of them, so that they also become rhombic dodecahedra. Repeat the process. This should make it clear how identical rhombic dodecahedra can be used to fill a three-dimensional volume without gaps. It may help to think of this like a 3D chess board where each dark cube is the core of a rhombic dodecahedron, and each white cube provides one pyramid to each adjoining dark cube.
From six directions (perpendicular to the faces of the ‘inner cube’ cube) a rhombic dodecahedron has a tilted square silhouette (projection), and shows four of its faces (the apex of one pyramid and the sides of four others). From eight directions (looking directly at the corners of the ‘inner cube’) a rhombic dodecahedron has a hexagonal silhouette, and shows three of its faces (arranged around the cube’s corner). This happens to be a way in which bees often cap the end of honeycomb.
Also of note is that in four spatial dimensions the rhombic dodecahedron is called a hyperdiamond, and becomes a Platonic Solid in this dimension. Platonic Solid is the name traditionally given to something whose edges and angles are all identical. A rhombic dodecahedron has identical faces and identical edges, but there are two different angles involved in its faces. It takes an extra spatial dimension to give space to allow these to become identical. It is probable that the rhombic dodecahedron’s exclusion from the 3D Platonic Solid list (described in Euclid’s ‘Thirteen Books of the Elements’, Book 13) has led to its unfamiliarity with today’s public.
From six directions (perpendicular to the faces of the ‘inner cube’ cube) a rhombic dodecahedron has a tilted square silhouette (projection), and shows four of its faces (the apex of one pyramid and the sides of four others). From eight directions (looking directly at the corners of the ‘inner cube’) a rhombic dodecahedron has a hexagonal silhouette, and shows three of its faces (arranged around the cube’s corner). This happens to be a way in which bees often cap the end of honeycomb.
Also of note is that in four spatial dimensions the rhombic dodecahedron is called a hyperdiamond, and becomes a Platonic Solid in this dimension. Platonic Solid is the name traditionally given to something whose edges and angles are all identical. A rhombic dodecahedron has identical faces and identical edges, but there are two different angles involved in its faces. It takes an extra spatial dimension to give space to allow these to become identical. It is probable that the rhombic dodecahedron’s exclusion from the 3D Platonic Solid list (described in Euclid’s ‘Thirteen Books of the Elements’, Book 13) has led to its unfamiliarity with today’s public.
Establishing the Anglo-Saxons knew of the rhombic dodecahedron
It is fair to assume that the beautiful flawless gem-grade garnet crystal material seen in, for example, the Sutton Hoo treasure and the Staffordshire Hoard, could have been traded as raw stones, and that some of these were likely euhedral examples (meaning, expressing the crystal’s habit). If the purer a crystal is the less likelihood there is for something to obscure its habit, we may be confident the habit of garnet was known; but we do not have to rely on this expectation alone, for there is an example of a model of a whole rhombic dodecahedron from Maldon, Essex (Portable Antiquities Scheme, Unique ID: SUSS-3C8EA4) which is incontestable proof that this solid was known in England before the Renaissance.
The date range for the object is recorded as 1000 to 1300 CE, but this is based on some stylistic comparisons with a small set of objects that appear visually related, and ‘No exact parallel for this object could be found’. The object is clearly a Christian holy water sprinkler, also known as a mace or an aspergillum, because it is hollow, socketed for a handle, and has holes in its side. Moreover, two of its rhombic sides have branching designs that match the growth habit of the shrub Hyssopus officinalis (hyssop), and its square socket matches the stem cross section of this shrub. Psalm 51 in the Bible talks of purging with a plant that has been traditionally translated or identified as hyssop, so the features on the copper alloy object that correspond with this establish its identification.
Roman cast copper-alloy (pentagonal) knobbed 'dodecahedron' from Hertfordshire (BH-692011) — one of a number of similar enigmatic objects from Britain and other northern provinces of the Roman Empire in the 1st-4th centuries CE. Fittock, M (2019) . Image CC. Portable Antiquities Scheme
BH-692011 is another recorded copper alloy hollow model of a ‘solid’ with pierced sides, but which has been dated to the Roman occupation of Britain (first to fourth centuries CE). This is a pentagonal dodecahedron (the fifth Platonic solid in three dimensions), and has knops or bobbles on its vertices similar to those on the holy water sprinkler. Such knops may represent heavenly bodies arranged around a Ptolemaic celestial shell (cf. Secrets of the Stones Part 1). This class of Roman object (mostly limited to Britain and other northern provinces of the Roman Empire) has been the subject of much study and speculation since there have been numerous excavated and contextually and stylistically dated examples, amounting to a non-trivial phenomenon.
The remainder of the faces of the rhombic dodecahedron which the Maldon holy water sprinkler models have bars that trace the long and short (length and width) paths between the vertices of the object (and the corners of the lozenges). The relationship of these, as has been discussed, is a ratio of one to the square root of two, but there is another mathematical significance that can help locate the Maldon object in a wider field of contemporary material culture.
The remainder of the faces of the rhombic dodecahedron which the Maldon holy water sprinkler models have bars that trace the long and short (length and width) paths between the vertices of the object (and the corners of the lozenges). The relationship of these, as has been discussed, is a ratio of one to the square root of two, but there is another mathematical significance that can help locate the Maldon object in a wider field of contemporary material culture.
In the attached video, we can see how marking the widths across the lozenges highlights the edges of the ‘inner cube’ (onto which square-based pyramids have been added). Likewise, marking the lengths across the lozenges highlights the edges of an octahedron (onto which triangular-based pyramids have been added).
We rely on 3D digital graphics, here, because the relationship between these shapes is far easier to intuit visually than by description or mathematical proof alone. Studying the digital reconstruction of the Maldon holy water sprinkler below, it is easy to see its square and hexagonal projections, its inner cube in the framework, made into a rhombic dodecahedron by addition of pyramids, but also its inner octahedron, made into a rhombic dodecahedron by the addition of tetrahedra. Handling, or looking around this object would provide these insights at least as effectively as studying these graphics. Though it had a ritual function, the Maldon sprinkler is thus a powerful learning technology for the reproduction of mathematical and philosophical knowledge.
Another solid that combines the cube and the octahedron is the cube-octahedron or cuboctahedron, which we find in abundance in the archaeological record. The cuboctahedron is a midway solid between a cube and an octahedron, and can be formed by measuring halfway along the sides of either, and lopping off the corners. In this way a single cuboctahedron twins a particular size of cube and a particular size of octahedron, and it is this twinned pair that we see in the rhombic dodecahedron and the bars of the Maldon holy water sprinkler.
The link between these solids causes us to take the ubiquity of the cuboctahedron in Roman and Anglo-Saxon jewellery more seriously than has hitherto been the case. Pins described as ‘polyhedral’ or ‘faceted-headed’ occur in both Roman and early Anglo-Saxon contexts, but become the predominant type of dress-pin across Britain during the eighth century, coinciding with the development of lozenge-brooches. The heads of these pins are most commonly cuboctahedral. Examples include SUR-A551E7 from Hampshire, YORYM-F9D484 from York and KENT-F499EE from Kent.
The link between these solids causes us to take the ubiquity of the cuboctahedron in Roman and Anglo-Saxon jewellery more seriously than has hitherto been the case. Pins described as ‘polyhedral’ or ‘faceted-headed’ occur in both Roman and early Anglo-Saxon contexts, but become the predominant type of dress-pin across Britain during the eighth century, coinciding with the development of lozenge-brooches. The heads of these pins are most commonly cuboctahedral. Examples include SUR-A551E7 from Hampshire, YORYM-F9D484 from York and KENT-F499EE from Kent.
Three examples of Anglo-Saxon 'Polyhedral pins' from the Portable Antiquities Scheme, dated 700-900 CE. left to right: SUR-A551E7 (CC. Surrey County Council). YORYM-F9D484 (CC. York Museums Trust) and KENT-F499EE (CC. Kent County Council)
The mathematical connection between the cuboctahedron, the rhombic dodecahedron and the way the Maldon holy water sprinkler has been designed, all leads to opening-up the question of the object’s date; however the date is not as important as the consistency and continuity of the learning it implies.
Partial examples
In addition to the Maldon holy water sprinkler and the abundant cuboctahedra seen on pins and other copper alloy jewellery, parts of the rhombic dodecahedron appear all across Anglo-Saxon art, and this was a key subject of our articles leading up to this one.
In Secrets in the Stones Part 2 (available here) Ædmund Thompson comprehensively explores the weight placed on the lozenge shape (and the tilted square shape) in Anglo-Saxon art and architecture. The lozenge represents one face of the rhombic dodecahedron, whilst the tilted square relates to either its internal geometry or to its methods of construction. The cross-within-lozenge motif (like faces of the Maldon holy water sprinkler) seen across Anglo-Saxon art thus represents the relationship between the cube, octahedron, tetrahedron and square pyramid via the rhombic dodecahedron.
In Secrets in the Stones Part 2 (available here) Ædmund Thompson comprehensively explores the weight placed on the lozenge shape (and the tilted square shape) in Anglo-Saxon art and architecture. The lozenge represents one face of the rhombic dodecahedron, whilst the tilted square relates to either its internal geometry or to its methods of construction. The cross-within-lozenge motif (like faces of the Maldon holy water sprinkler) seen across Anglo-Saxon art thus represents the relationship between the cube, octahedron, tetrahedron and square pyramid via the rhombic dodecahedron.
In Secrets in the Stones Part 3 (available here) Ædmund Thompson covers both jewellery and architecture. Not only do Rhenish Helm roofs straightforwardly represent one half of a rhombic dodecahedron, with the tower providing its square projection, but several surviving Anglo-Saxon copper alloy censers (used in church to burn frankincense) have the Rhenish Helm roof type in their design, and resemble the upper portions of the Maldon holy water sprinkler.
The linked article finds this roof design depicted in a sword fitting from the Staffordshire Hoard - a representation of the rhombic dodecahedron using worked garnets themselves, pushing awareness of this form deep into early Anglo-Saxon history.
We decided to invest in the articles leading to this one to speed up the grand reveal in this article, but they were written in full knowledge if the conclusions reached here.
We decided to invest in the articles leading to this one to speed up the grand reveal in this article, but they were written in full knowledge if the conclusions reached here.
A more complex geometry in millefiori
The abundant mention of pyramids within this article will naturally cause us to speculate as to whether the choice of the pyramid shape for early Anglo-Saxon ‘sword pyramids’ (mounts associated with scabbards) was informed by garnet geometry. Regardless of our confidence level in making this connection (and indeed speculation as to which pyramids involved at different stages of meditation on the rhombic dodecahedron the sword pyramids represented), the art of one matching pair of seventh-century sword pyramids is exceptionally clear in its connection to garnet geometry.
Staffordshire Hoard gold and garnet cloisonne 'sword pyramids' Cat 578 & Cat 579 featuring millefiori glass at the apex (Image from Staffordshire Hoard catalogue; "The Staffordshire Hoard: an Anglo-Saxon Treasure" Barbican Research Associates, 2017. Updated 2019. Funded by Historic England and the Archaeology Data Service. Used here under a modified CC BY-NC-S(PD) licence as per ADS Terms of Use
Staffordshire Hoard Cat 578 & 579 each has a piece of millefiori glass set into its flat apex, featuring a design in opaque white and red glass. The design has a 3x3 chequerboard (which we have taken to calling a nine grid), with the centre square and corner squares in the ruby red, and the four middle-side squares being white. Each of the white squares has an X in the red glass trailed through it. The way millefiori glass is manufactured is by fusing canes of coloured glass together, and then drawing them out, sometimes folding or adding canes, till the stretched-out molten glass forms a thin cane of different colours that can be cut to show off its cross section as miniature art.
Author with a scaled-up replica of the millefiori apices of Staffordshire Hoard pyramids Cat 578 & Cat 579. Lecture prop produced by glass specialist Caroline Weidman, Wiedman Glass, Essex
It is worth stating how much skill and effort contributes to the making of a millefiori item of this quality, and looking for craftspeople to replicate the work on today’s art scene (I have been informed by a professional) might take one as far afield as Murano, Venice.
The design is likely therefore to have been of importance, considering the pains taken to achieve it. Ignoring the geography of the current art glass scene, the likelihood the glass was of Anglo-Saxon manufacture (or focused on an Anglo-Saxon market) is enhanced by comparisons with the millefiori work in the Sutton Hoo treasure, in particular in the shoulder clasps, where the same design of nine grid and Xs can be seen, but made from different glass canes.
This star-like pattern is popular in Latvia, and is known as the Auseklis. Owing to its having been found there in prehistoric contexts, it is something of a national symbol. It is beyond the scope of this article to examine international links relating to the symbol, but from here the shape will be referred to as the Auseklis.
Returning to an earlier section of this article, we can reflect how in our 3D chessboard, the Staffordshire Hoard Auseklis gives a helpful cross section of rhombic dodecahedra filling 3D space, as well as a guide to constructing one by projecting a tilted square through each face of a cube, as shown in the videos below.
The design is likely therefore to have been of importance, considering the pains taken to achieve it. Ignoring the geography of the current art glass scene, the likelihood the glass was of Anglo-Saxon manufacture (or focused on an Anglo-Saxon market) is enhanced by comparisons with the millefiori work in the Sutton Hoo treasure, in particular in the shoulder clasps, where the same design of nine grid and Xs can be seen, but made from different glass canes.
This star-like pattern is popular in Latvia, and is known as the Auseklis. Owing to its having been found there in prehistoric contexts, it is something of a national symbol. It is beyond the scope of this article to examine international links relating to the symbol, but from here the shape will be referred to as the Auseklis.
Returning to an earlier section of this article, we can reflect how in our 3D chessboard, the Staffordshire Hoard Auseklis gives a helpful cross section of rhombic dodecahedra filling 3D space, as well as a guide to constructing one by projecting a tilted square through each face of a cube, as shown in the videos below.
After seeing the Auseklis shape explicitly displayed in the millefiori, other designs in the jewellery appear as connected (but less clear) representations of the same concepts. For instance, the Staffordshire Hoard Cat 572 & 573 pair of sword pyramids (blow) have the square-within-tilted-square motif suddenly show up when viewed from above, as triangular gold designs on the side faces of the truncated pyramid form gain a new geometry from this perspective.
This feature is shared by the pair from the Sutton Hoo Mound 17 sword (BM 1991,0411.2853 &4), and the countless non-jewelled pyramids of Mortimer’s most abundant type 1vi - defined by incised or inlaid triangles which behave as just described. A majority of pyramids found in England are of this type, representing a non-trivial phenomenon, but the design has not been hitherto explained.
Likewise, Cat 580 & 581 have an X in gold amid garnets at its flat apex, and this appears to be an important shape. Added to these, the Sutton Hoo Mound 1 sword pyramids (BM 1939,1010.28 & 29) have 25 grid chequerboards which gain significance in spite of not displaying Xs.
Likewise, Cat 580 & 581 have an X in gold amid garnets at its flat apex, and this appears to be an important shape. Added to these, the Sutton Hoo Mound 1 sword pyramids (BM 1939,1010.28 & 29) have 25 grid chequerboards which gain significance in spite of not displaying Xs.
Most of these examples date from the early conversion period (the first quarter of the seventh century CE), with some such as the Sutton Hoo Mound 17 examples predating the mission of St Augustine (597 CE) therefore evidencing pre-Christian Anglo-Saxon engagement with these concepts.
An extremely explicit example of the X shape grouping in fours to delineate a tilted square is found on a gold shilling found near Harrogate in 2012 (EMC number 2012.0025). The monarch for whom it was minted is not recorded on the coin, but a date range is given of 600 to 867 CE. The obverse shows a stylised bearded man (perhaps Christ or an evangelist) standing between two long crosses.
Gold 'York Group' shilling / thrymsa found in Harrogate. 7-9th century CE. EMC number : 2012.0025. CC. Fitzwilliam Museum, Cambridge.
The reverse has a symmetrical design of four Dæg (day) runes, which serve as our Xs, on the outside of a ring. These are separated by four equilateral crosses with slightly pronounced round terminals. Inside the ring, at the centre of the design, is a small tilted square lined up with the open triangular bottoms of the dæg runes. From this tilted square sprout lines that connect it to the circle, creating triangles that compliment the geometry of the runes, and turn the central section into a kind of cross.
Looking at the geometric proofs (diagrams and videos) in this article, we can see how the use of the Auseklis on each side of a cube can be used to project tilted square rays or beams. Four Xs are required on each of the six faces of the cube, and this gives a total of 24 (the number of runes in the Elder Futhark). The choice within the runic system to employ a word associated with time to a device used to construct the rhombic dodecahedron is something to note, considering the later history of this geometry in English art.
Looking at the geometric proofs (diagrams and videos) in this article, we can see how the use of the Auseklis on each side of a cube can be used to project tilted square rays or beams. Four Xs are required on each of the six faces of the cube, and this gives a total of 24 (the number of runes in the Elder Futhark). The choice within the runic system to employ a word associated with time to a device used to construct the rhombic dodecahedron is something to note, considering the later history of this geometry in English art.
A thirteenth-century Anglo-Saxon revival
There was something of a renaissance in Anglo-Saxon culture during the reign of Henry III. The young son and successor of King John found himself crowned unexpectedly at Gloucester on 28 October 1216 whilst war was raging on English soil both with baronial and French expeditionary forces. Henry consolidated his power base by appealing both to the Church and the English people in general, and was generous in his relief for the poor. As part of this, he focused religious devotions upon the Anglo-Saxon king Edward the Confessor as a royal saint, translating his remains within Westminster Abbey to a lavish shrine and extracting in the process a suite of late Anglo-Saxon regalia which formed the foundation of the English coronation jewellery down to the destruction of the Civil War in the seventeenth century.
At Westminster Henry constructed a coronation theatre centred on a square pavement (known as the Cosmati Pavement) at whose centre is the spot where the act of coronation has taken place ever since Henry’s second coronation on 17 May 1220.
At Westminster Henry constructed a coronation theatre centred on a square pavement (known as the Cosmati Pavement) at whose centre is the spot where the act of coronation has taken place ever since Henry’s second coronation on 17 May 1220.
Researching this topic several years ago I had made the observation that the Auseklis appears many times in the Cosmati Pavement as well as the lapidary work on the tomb of Henry III and the shrine of St Edward, but my partner James Syrett has further realised that the geometry of the pavement itself conforms exactly to the Auseklis.
The author holding a print of the overhead view of the Cosmati Pavement now possible from the Diamond Jubilee Gallery, marked up to show that the design as a whole presents an Auseklis within nine-grid, like the Staffordshire Hoard pyramid apex millefiori.
Considering the design more deeply, I realised that all the roundels in the design are substantially different, except for the four grouped around the sides of the pavement’s large tilted square, which all feature hexagons. This corresponds to the four hexagonal projections of the rhombic dodecahedron, that are perpendicular to the faces of an octahedron in the way the tilted square projections are to the cube.
Thinking about projecting beams of light forming a rhombic dodecahedron leads us to consider the Westminster Retable (a richly decorated piece of sculptured board amusingly described as a sort of splashback to the altar table). There is more information about this on the website for Westminster Abbey (here), where it is on display in the Queen’s Diamond Jubilee Galleries.
The upper portion of the central section contains mosaic work in red and blue glass. Blue octagons separate red tilted squares that would glint and shine down the length of the abbey. The attached video shows how this pattern is also a cross section of a volume filled with rhombic dodecahedra.
Thinking about projecting beams of light forming a rhombic dodecahedron leads us to consider the Westminster Retable (a richly decorated piece of sculptured board amusingly described as a sort of splashback to the altar table). There is more information about this on the website for Westminster Abbey (here), where it is on display in the Queen’s Diamond Jubilee Galleries.
The upper portion of the central section contains mosaic work in red and blue glass. Blue octagons separate red tilted squares that would glint and shine down the length of the abbey. The attached video shows how this pattern is also a cross section of a volume filled with rhombic dodecahedra.
'Scutum fidei' / Shield of Faith (Public Domain)
The centrality of the Christological drama of the eucharist (communion) at the altar makes the red tilted square beams connected to Jesus. Meanwhile, the mediaeval mind associated the Virgin Mary with the epithet ‘polorum regina’ or queen of the poles, depicting her with a starry mantle; and God the Father could be associated with the classical Apollo and the noonday sun. In a cruciform church this corresponds to the transepts, and in the eastern transepts at Christchurch Canterbury (the cathedral), the round windows there have tilted square panels of leaded glass in the centre, supported by ironwork. The third beam through the cube is a vertical one, and this accounts for the Cosmati Pavement, as well as the tilted square shapes made by the vaulting of crossing towers. The vertical dimension is associated with the Holy Spirit, as a baptism of light or fire at Pentecost.
There is an allegorical implication in this geometry that the unity of God is experienced as a Trinity according to the projection along which God is approached, and this may have influenced the famous ‘scutum fidei’ (shield of faith) heraldic device which depicts God named in the centre, and three bands (labelled ‘est’ (is)) connecting the three persons of the Trinity (The Father, The Son, and The Holy Spirit). The coronation theatre is therefore geometrically described as being a concentrated or focused holy place, via art and architecture. The late mediaeval coronation is therefore something of a communion with the divine more akin to Pentecost than baptism, but containing the same demand for a special place.
There is an allegorical implication in this geometry that the unity of God is experienced as a Trinity according to the projection along which God is approached, and this may have influenced the famous ‘scutum fidei’ (shield of faith) heraldic device which depicts God named in the centre, and three bands (labelled ‘est’ (is)) connecting the three persons of the Trinity (The Father, The Son, and The Holy Spirit). The coronation theatre is therefore geometrically described as being a concentrated or focused holy place, via art and architecture. The late mediaeval coronation is therefore something of a communion with the divine more akin to Pentecost than baptism, but containing the same demand for a special place.
Unlocking the Anglo-Saxon world through Henry III’s revival
The Mercian royal church of St Wystan’s, Repton, Derbyshire, has been discussed already in this series, but there are details that have been withheld until this article as they make sense in the context of the rhombic dodecahedron, and the thirteenth-century works at Westminster Abbey.
The first thing to note is that as soon as the idea has been understood that the groins or ribs of a vault can be connected to an important geometric symbolism in defining the division of space beneath, Repton’s nine grid gains the Xs that define a large tilted square that penetrates between its famous four spiralled columns.
The first thing to note is that as soon as the idea has been understood that the groins or ribs of a vault can be connected to an important geometric symbolism in defining the division of space beneath, Repton’s nine grid gains the Xs that define a large tilted square that penetrates between its famous four spiralled columns.
The high altar, in a double-height space above the crypt, thus conceivably occupies the centre of a rhombic dodecahedron using this projection. It is possible that this was intended to be appreciated as something special within the crypt, or as an intensification of the space above. Much later buildings, such as the late ninth-century (post-Alcuin of York) ‘Westwerk’ at Corvey Abbey in Francia (now in Germany), the Mercian crypt/chapel at St Oswald’s, Gloucester, and the chapter house of the old St Paul’s in London, utilised the theme of a nine-grid vaulted undercroft with four pillars supporting an important royal or civic religious space above.
The second thing to note is how a unique feature of the design of Westminster’s Cosmati Pavement is its use of thick, dark Purbeck marble bands delineating the design. Whilst it is now clear how this feature helps the readability of the Auseklis, the origin of the aesthetic has not been very clearly explained in the literature around the pavement. At Repton, however, the surviving floor is very sunken, irregular and uneven, but with a level (dark) stone sill around part of the edge of the room. Could it be that the floor once had a mosaic pavement of the kind that was consistently being produced in the Mediterranean world at that time? Part of the presentation of the mosaic theory for the original floor treatment at Repton is the idea that Henry III or his designers visited Repton specifically looking for inspiration. This article asserts the theory that this event did occur ‒ that the Cosmati Pavement is a direct evocation of Repton as part of Henry III’s Anglo-Saxonism.
The third thing to note is that the average measurement given in the literature for the internal dimensions of the crypt is 16 feet by 16 feet. This measurement corresponds with the inner square of the Cosmati Pavement.
The second thing to note is how a unique feature of the design of Westminster’s Cosmati Pavement is its use of thick, dark Purbeck marble bands delineating the design. Whilst it is now clear how this feature helps the readability of the Auseklis, the origin of the aesthetic has not been very clearly explained in the literature around the pavement. At Repton, however, the surviving floor is very sunken, irregular and uneven, but with a level (dark) stone sill around part of the edge of the room. Could it be that the floor once had a mosaic pavement of the kind that was consistently being produced in the Mediterranean world at that time? Part of the presentation of the mosaic theory for the original floor treatment at Repton is the idea that Henry III or his designers visited Repton specifically looking for inspiration. This article asserts the theory that this event did occur ‒ that the Cosmati Pavement is a direct evocation of Repton as part of Henry III’s Anglo-Saxonism.
The third thing to note is that the average measurement given in the literature for the internal dimensions of the crypt is 16 feet by 16 feet. This measurement corresponds with the inner square of the Cosmati Pavement.
Westminster Cosmati Pavement overlaid with the plan of the Mercian / Anglo-Saxon royal mausoleum / baptistry at Repton (Animation by Æd Thompson). The pavement's central square is precisely the same dimensions as the interior of the Repton room, with the pavement's 'tombs' corresponding to the crypt's loculi
Fourthly, the rectangular panels (traditionally referred to as ‘tombs’) that occupy the centre of each side of the broad border to the Cosmati Pavement divide the pavement into thirds both ways, giving us our nine grid, but they also correspond to the niches or bays that pierce into or through the walls of the crypt at Repton, and have also been traditionally connected with the idea of ‘loculi’ or places for burials to be deposited, in the crypt’s assumed role of royal and saintly mausoleum.
If these niches are, however, windows, we again see ecclesiastical architecture creating opportunities for light to intersect at 90 degrees, imbuing the central part of the space with a special glow that the dark corners of the room (where the crypt is entered) would not have.
Oddly this arrangement is also reminiscent of the sword pyramids.
If these niches are, however, windows, we again see ecclesiastical architecture creating opportunities for light to intersect at 90 degrees, imbuing the central part of the space with a special glow that the dark corners of the room (where the crypt is entered) would not have.
Oddly this arrangement is also reminiscent of the sword pyramids.
Early c7th CE gold and garnet cloisonne pyramids with apexes highlighted (left to right): Staffordshire Hoard Cat 572. Sutton Hoo Mound 1 (1939,1010.29. CC. British Museum) and Staffordshire Hoard Cat 578. (Image from Staffordshire Hoard catalogue; "The Staffordshire Hoard: an Anglo-Saxon Treasure" Barbican Research Associates, 2017. Updated 2019. Funded by Historic England and the Archaeology Data Service. Used here under a modified CC BY-NC-S(PD) licence as per ADS Terms of Use
Effigy, tomb of Henry III with tilted-square-on-square cushion arrangement (CC. Valerie McGlinchey. Wikimedia Commons)
The Sutton Hoo pyramids and the Staffordshire Hoard Cat 572 & 573 pair all have gold lines emanating from the square panels of their apex inlays. In the Staffordshire Hoard Cat 578 & 579 pair ‒ our most explicit pair ‒ there is a rectangular garnet inset into each top edge of the truncated pyramids, creating exactly the same effect as a plan of the Repton crypt, or simply a view of the Cosmati Pavement.
Pictorial or symbological representation of a building via a birds-eye-view plan was known to the early Anglo-Saxons, as evidenced by the plan of the Temple of Solomon in the Codex Amiatinus, produced in Jarrow in the late seventh century.
The garnets potentially represent beams of red light coming in from the sides of a cube, complementing the tilted square in the millefiori glass that gives us the vertical dimension (like the Cosmati Pavement does). Incidentally, this gives rise to our wondering about the iconography of the red cross in the evangelists’ portrait page in the eighth-century Lichfield Gospels, as well as the Flag of the Resurrection (red cross on white field) that become used as a badge in the time of Henry III and eventually became associated with St George and England itself.
A fifth thing to note is the tomb of Henry III ‒ how it potentially corroborates these observations with its combination of spiralled columns and panelled pilasters, along with its continuation of the same rich geometry in its mosaic work, and the striking fact of a square and tilted square cushion arrangement supporting the head of the royal effigy (a trend repeated by the tomb of Edward III on the other side of the sanctuary).
Pictorial or symbological representation of a building via a birds-eye-view plan was known to the early Anglo-Saxons, as evidenced by the plan of the Temple of Solomon in the Codex Amiatinus, produced in Jarrow in the late seventh century.
The garnets potentially represent beams of red light coming in from the sides of a cube, complementing the tilted square in the millefiori glass that gives us the vertical dimension (like the Cosmati Pavement does). Incidentally, this gives rise to our wondering about the iconography of the red cross in the evangelists’ portrait page in the eighth-century Lichfield Gospels, as well as the Flag of the Resurrection (red cross on white field) that become used as a badge in the time of Henry III and eventually became associated with St George and England itself.
A fifth thing to note is the tomb of Henry III ‒ how it potentially corroborates these observations with its combination of spiralled columns and panelled pilasters, along with its continuation of the same rich geometry in its mosaic work, and the striking fact of a square and tilted square cushion arrangement supporting the head of the royal effigy (a trend repeated by the tomb of Edward III on the other side of the sanctuary).
A philosophical reading
It is important to be clear-headed about what the evidence of the Cosmati Pavement implies. There is strong evidence that as part of his political and religious programme, which revolved around the veneration of an historic Anglo-Saxon king as a saint, Henry III took Repton as a model for a coronation theatre that suited his vision for England. This does not necessarily mean that Repton was used in this way in the Anglo-Saxon period itself. The support for this must therefore come from within the Anglo-Saxon period, and the role of the lozenge and the Auseklis (as well as Rhenish Helm shapes) have so far offered a good start in establishing this hypothesis as theory. Nevertheless, the Cosmati Pavement is such an explicit art document that it can help offer insights against which earlier evidence may be assessed in our developing discourse.
The chief foundation of this is the set of inscriptions in the pavement. (Details and visiting information may be found here.)
The chief foundation of this is the set of inscriptions in the pavement. (Details and visiting information may be found here.)
In the year of Christ one thousand two hundred and twelve plus sixty minus four, the third King Henry, the city, Odoricus and the abbot put these porphyry stones together.
If the reader wisely considers all that is laid down, he will find here the end of the primum mobile; a hedge (lives for) three years, add dogs and horses and men, stags and ravens, eagles, enormous whales, the world: each one following triples the years of the one before.
The spherical globe here shows the archetypal macrocosm.
The way that the number three is repeatedly emphasised is key, and so is the concept of a sort of fractal, expanding nature to the lengths of time referenced. First, however, it pays to see the pavement simply as a spatial depiction of time.
Christian theology sees God as existing outside of the constraints of linear time by which we, as mortals, are bound. So, a person viewing the Cosmati Pavement has a view representing the way God sees both time and space ‒ all spread out at once, crystallised in eternity. If each piece of the mosaic represents a person (their soul), we see the individuality of people in their different shapes and colours. The limits of a piece represent a mortal person’s limits both in space and in time. The different patterns in the different mosaic panels of the pavement thus represent different social contract organisations (kingdoms, civilisations ancient, present and future). At this zoomed-in scale, however, they are crudely symbolic ‒ the number of people anyone knows massively outstrips the number of stones adjoining one another directly. Even so, the pavement as a whole is bewildering in its complexity. It confronts a monarch at the moment of coronation with the sublime reality of God’s view, compared to their own relative inadequacy.
The rhombic dodecahedron is a Platonic Solid (a perfect shape) in four spatial dimensions (where it is called a hyperdiamond), and it is a reasonable technique of art to represent time allegorically using this extra spatial dimension. If you were to drop a ball through a 2D plane, somebody inhabiting that 2D world would see a line grow from a point and then diminish as the 3D ball passed through. Going around it, they would perceive that the object was circular, but the way it appeared, grew, diminished and vanished would appear very odd. If a 4D person dropped a 4D ball through our three dimensions, we would see a ball swell from nothing, diminish, then vanish. If a 4D person dropped the hyperdiamond ‒ this special Platonic Solid ‒ through our three dimensions, we would see a rhombic dodecahedron swell from nothing. This swelling effect is echoed in the Cosmati Pavement inscription, and the obsession with threes makes sense given the 3x3 nature of the nine grid used to conceptualise a hovering volume of space that could represent some substance from the world of the 4D person ‒ God in the Kingdom of Heaven ‒ that might equate to some notion of Divine Grace or a visitation by the Holy Spirit in the manner of the light or fire of Pentecost.
The connection of space and time (cosmology) with the rhombic dodecahedron is likely anchored by Plato’s work known as ‘Timaeus’. It is very necessary to take a long passage from Desmond Lee’s translation:
Christian theology sees God as existing outside of the constraints of linear time by which we, as mortals, are bound. So, a person viewing the Cosmati Pavement has a view representing the way God sees both time and space ‒ all spread out at once, crystallised in eternity. If each piece of the mosaic represents a person (their soul), we see the individuality of people in their different shapes and colours. The limits of a piece represent a mortal person’s limits both in space and in time. The different patterns in the different mosaic panels of the pavement thus represent different social contract organisations (kingdoms, civilisations ancient, present and future). At this zoomed-in scale, however, they are crudely symbolic ‒ the number of people anyone knows massively outstrips the number of stones adjoining one another directly. Even so, the pavement as a whole is bewildering in its complexity. It confronts a monarch at the moment of coronation with the sublime reality of God’s view, compared to their own relative inadequacy.
The rhombic dodecahedron is a Platonic Solid (a perfect shape) in four spatial dimensions (where it is called a hyperdiamond), and it is a reasonable technique of art to represent time allegorically using this extra spatial dimension. If you were to drop a ball through a 2D plane, somebody inhabiting that 2D world would see a line grow from a point and then diminish as the 3D ball passed through. Going around it, they would perceive that the object was circular, but the way it appeared, grew, diminished and vanished would appear very odd. If a 4D person dropped a 4D ball through our three dimensions, we would see a ball swell from nothing, diminish, then vanish. If a 4D person dropped the hyperdiamond ‒ this special Platonic Solid ‒ through our three dimensions, we would see a rhombic dodecahedron swell from nothing. This swelling effect is echoed in the Cosmati Pavement inscription, and the obsession with threes makes sense given the 3x3 nature of the nine grid used to conceptualise a hovering volume of space that could represent some substance from the world of the 4D person ‒ God in the Kingdom of Heaven ‒ that might equate to some notion of Divine Grace or a visitation by the Holy Spirit in the manner of the light or fire of Pentecost.
The connection of space and time (cosmology) with the rhombic dodecahedron is likely anchored by Plato’s work known as ‘Timaeus’. It is very necessary to take a long passage from Desmond Lee’s translation:
In the first place it is clear to everyone that fire, earth, water and air are bodies, and all bodies are solids. All solids are again bounded by surfaces, and all rectilinear surfaces are composed of triangles. There are two basic types of triangle, each having one right angle and two acute angles: in one of them these two angles are both half right angles, being subtended by equal sides, in the other they are unequal, being subtended by unequal sides. This we postulate as the origin of fire and the other bodies, our argument combining likelihood and necessity; their more ultimate origins are known to god and to men whom god loves. We must proceed to inquire what are the four most perfect possible bodies which, though unlike each other, are some of them capable of transformation into each other on resolution. If we can find the answer to this question we have the truth about the origin of earth and fire and the two mean terms between them; for we will never admit that there are more perfect visible bodies than these, each in its type. So we must do our best to construct four types of perfect body and maintain that we have grasped their nature sufficiently for our purpose. Of the two basic triangles, then, the isosceles has only one variety, the scalene an infinite number. We must therefore choose, if we are to start according to our own principles, the most perfect of this infinite number. If anyone can tell us of a better choice of triangle for the construction of the four bodies, his criticism will be welcome; but for our part we propose to pass over all the rest and pick on a single type, that of which a pair compose an equilateral triangle. It would be too long a story to give the reason, but if anyone can produce a proof that it is not so we will welcome his achievement. So let us assume that these are the two triangles from which fire and the other bodies are constructed, one isosceles and the other having a greater side whose square is three times that of the lesser. We must now proceed to clarify something we left undetermined a moment ago. It appeared as if all four types of body could pass into each other in the process of change; but this appearance is misleading. For, of the four bodies that are produced by our chosen types of triangle, three are composed of the scalene, but the fourth alone from the isosceles. Hence all four cannot pass into each other on resolution, with a large number of smaller constituents forming a lesser number of bigger bodies and vice versa; this can only happen with three of them. For these are all composed of one triangle, and when larger bodies are broken up a number of small bodies are formed of the same constituents, taking on their appropriate figures; and when small bodies are broken up into their component triangles a single new figure may be formed as they are unified into a single solid.
Plato as represented in Raphael’s 1511 'School of Athens' fresco in the Vatican apartments. The huge fresco centres, and through forced perspective, focuses on a debating Aristotle and Plato (left) who, curiously, is shown carrying his relatively obscure work 'Timaeus'
So much for their transformation into each other. We must next describe what geometrical figure each body has and what is the number of its components. We will begin with the construction of the simplest and smallest figure. Its basic unit is the triangle whose hypotenuse is twice the length of its shorter side. If two of these are put together with the hypotenuse as diameter of the resulting figure, and if the process is repeated three times and the diameters and shorter sides of the three figures are made to coincide in the same vertex, the result is a single equilateral triangle composed of six basic units. And if four equilateral triangles are put together, three of their plane angles meet to form a single solid angle, the one which comes next after the most obtuse of plane angles: and when four such angles have been formed the result is the simplest solid figure, which divides the surface of the sphere circumscribing it into equal and similar parts.
The second figure is composed of the same basic triangles put together to form eight equilateral triangles, which yield a single solid angle from four planes. The formation of six such solid angles completes the second figure.
The third figure is put together from one hundred and twenty basic triangles, and has twelve solid angles, each bounded by five equilateral plane triangles, and twenty faces, each of which is an equilateral triangle.
After the production of these three figures the first of our basic units is dispensed with, and the isosceles triangle is used to produce the fourth body. Four such triangles are put together with their right angles meeting at a common vertex to form a square. Six squares fitted together complete solid angles, each composed by three plane right angles. The figure of the resulting body is the cube, having six plane square faces.
There still remained a fifth construction, which the god used for embroidering the constellations on the whole heaven.
(Plato's Timaeus. Translation by Desmond Lee)
Since the fifth 3D Platonic Solid is the pentagonal dodecahedron, and since Roman dodecahedra have been archaeologically described, as mentioned above, it has been widely assumed that Plato referred to this when he wrote of the ‘fifth construction’. However, the speculations in ‘Timaeus and Critias’ relating to cosmology are tied to Plato’s meditations on a perfect society (and the allegorical story of Atlantis, for which this work is chiefly known).
The rhombic dodecahedron can fulfil a role similar to that of the ashlar cube in the allegory of Freemasonry. That is, if the stone represents a person, they can fit together in a perfect society as a ‘polished’ character, just as cubes can fit together and fill volumes. Yet the rhombic dodecahedron is more subtle, as it has both square and hexagonal projections, so one may need to be manipulated to find the right fit. Earlier I described how visualising a 3D chessboard may help in grasping the way this 3D tessellation works from the square projections mindset. From a different angle, the rhombic dodecahedra fit together like layers of honeycomb, offset to mesh together. The use of bees as social allegory is seen in both Anglo-Saxon and Frankish society, and has classical roots (for example, throughout Virgil’s Georgics, Book IV). The fertile ground for Plato’s social philosophy that the rhombic dodecahedron offers lends weight to our identification of his fifth solid at least as much as the observation that whereas garnet crystals commonly grow as rhombic dodecahedra, pentagonal dodecahedra are vanishingly rare in nature.
In a previous article in this series (here) I demonstrated evidence of knowledge of Plato’s ‘Timaeus’ and Ptolemy’s ‘Harmonics’ in the Sutton Hoo scabbard bosses. The present discussion is an area in which the ramifications of that work may bear substantial fruit.
The Cosmati Pavement places a heavy emphasis on the four hexagonal projections of the rhombic dodecahedron. We can see evidence of earlier engagement with hexagonal geometry in the ninth-century triumphal arch or gatehouse at the imperial abbey at Lorsch in Germany. Built in white and red stone, the parquetry of the facade follows Roman mosaic work and prefigures later lapidary work such as at Westminster Abbey.
The ‘king’s hall’ is carried above a processional way by arches whose threefold division and four piers echo Repton as much as Roman triumphal arches. In the spandrels of the arches there is an uneven red and white chequerboard of blocks. Each spandrel has 6 uneven red blocks, so each arch has 12 (the sides of the rhombic dodecahedron). Above this, there is a red and white chequerboard frieze of tilted squares. Each arch has a panel above it, containing 20 red tilted square blocks. On each facade, therefore, there are 36 of the spandrel blocks (the number of Decans, astrological deities representing a ten degree sweep of the sky), and 60 of the tilted squares (the number of degrees in each angle of an equilateral triangle, and one sixth of a circle). The walls of the king’s hall itself are decorated with a pattern made of red stone hexagons touching at their points, separated by white stone equilateral triangles. The pattern looks a lot like cells of honey separated by thick wax dividers in a honeycomb. The triangles add to the hexagons to be perceptible as hexagrams, and the joints between the stones represent this pattern as defined by three sets of parallel lines, at an angle of 60 degrees from each other. In other words, the monument encapsulates the shapes critical for the construction and understanding of the rhombic dodecahedron, as well as including optional numerology relating to Persian and classical astrology and astronomy, geometry and mathematics. Additionally, the tiered nature of the building, from uneven spandrel blocks below, to sophisticated hexagons and stars above, connects directly to Plato’s idea of Guardians as special people whose philosophical knowledge and virtue recommend them as natural leaders of an orderly society.
The use of the hexagram connects the ninth-century work at Lorsch directly to the culture of the Staffordshire Hoard and Sutton Hoo Auseklis glasswork. As shown in the attached diagram and videos, the treatment of the cube with the Auseklis can be mirrored by treating the connected octahedron in the same way. A division of its edges into thirds, and the connecting of these points with parallel lines, gives a hexagram whose inner hexagon will be a projection of the exact same rhombic dodecahedron as that produced by its twin using the Auseklis on the cube. Mere knowledge of projections of a rhombic dodecahedron would not offer up the hexagram as a preferred symbol.
The use of the hexagram connects the ninth-century work at Lorsch directly to the culture of the Staffordshire Hoard and Sutton Hoo Auseklis glasswork. As shown in the attached diagram and videos, the treatment of the cube with the Auseklis can be mirrored by treating the connected octahedron in the same way. A division of its edges into thirds, and the connecting of these points with parallel lines, gives a hexagram whose inner hexagon will be a projection of the exact same rhombic dodecahedron as that produced by its twin using the Auseklis on the cube. Mere knowledge of projections of a rhombic dodecahedron would not offer up the hexagram as a preferred symbol.
There is of course a known route for this information to have conceivably entered Francia from Anglo-Saxon England, which is via Alcuin of York, the head of Charlemagne’s court school, who among other things was noted as a mathematician. The desired corroboration of the idea that the hexagonal aspect of the rhombic dodecahedron was known to the Anglo-Saxons at an early date is provided partly by the pyramid mounts as representing one half of an octahedron. The sword pyramid Staffordshire Hoard Cat 581 has a garnet trefoil on each side of its truncated pyramid, hinting at the threefold symmetry of hexagonal projections through an octahedron. More explicitly, a middle Anglo-Saxon mount (LEIC-15A132) now held at the Melton Carnegie Museum, Melton Mowbray, features a sugarloaf shape with a hexagram at the apex, with lines streaming down the sides from the points of the hexagram. The central hexagon of this silver gilt object was speckled with ‘tiny punched triangles’ to sparkle. Similar hexagrams are seen on coins, particularly pennies of Charlemagne's contemporary, Offa of Mercia, typically with a small tilted square on the reverse.
A question remains: why is so much evidence of this phenomenon found on high-status jewellery (possibly regalia)? The answer can tentatively be suggested through the lens of the Cosmati Pavement. A coronation ritual sets a monarch apart from ordinary people as a figure imbued by an almost pentecostal or apostolic status. There are two broad approaches to reading the message of the rhombic dodecahedron. On the one hand, a heavily Christianised perspective may see the geometry as to do with the three beams of the ‘scutum fidei’ and the Trinity, and thus perhaps Divine Grace and the visitation of the Holy Spirit. On the other hand, a perspective rooted in classical (and perhaps Anglo-Saxon) Pagan philosophy and faith might centre upon Plato. In this reading, the rhombic dodecahedron, represented in the natural garnet crystal, connects with a general theme of social harmony and governance. Imbuing a person with this could establish their identity as a Guardian ‒ a person intrinsically worthy of leadership. Small and lower-value items, such as the cuboctahedral pins and non-elite examples of lozenge brooches, display a percolation of this aesthetic and philosophy through society, but lack the intense sophistication of royal and architectural work. Access to knowledge, and access to wearable goods (as both consumer goods and a means of transmitting knowledge), could have had a structural role within society.
Having reached this theory through Anglo-Saxon jewellery evidence, and not just through architecture, Henry III’s view of Repton as a coronation site can be thought of as reasonable, although the early jewellery evidence suggests that whilst broad concepts may have longevity, surface aesthetics may impede cultural legibility. The coronation we will witness in 2023 will not closely resemble any seventh-century initiation rituals to leadership, even though we are beginning to understand the strength of philosophical and liturgical continuity.
Having reached this theory through Anglo-Saxon jewellery evidence, and not just through architecture, Henry III’s view of Repton as a coronation site can be thought of as reasonable, although the early jewellery evidence suggests that whilst broad concepts may have longevity, surface aesthetics may impede cultural legibility. The coronation we will witness in 2023 will not closely resemble any seventh-century initiation rituals to leadership, even though we are beginning to understand the strength of philosophical and liturgical continuity.
Conclusion and epilogue
There is compelling evidence that the Anglo-Saxons’ love of the lozenge shape and other motifs derives from the natural habit of their favourite gemstone: the garnet crystal. It is not hard to appreciate how the natural habit of crystals ‒ especially those which take the form of Platonic Solids ‒ would have been a source of marvel to pre-industrial cultures, as indeed they still are today.
The millefiori glass in the Staffordshire Hoard and Sutton Hoo combines with the Maldon holy water sprinkler and the Rhenish Helm roofs to cement the rhombic dodecahedron as a significant piece of intellectual freight that holds substantial explanatory power within Anglo-Saxon (and Frankish) art and architectural history. This fundamental form is naturally embodied in an explicit way by whole garnets, and in a symbolic (or occult) manner by use of this material.
Our new understanding of this geometry, and its central role in the meaning of thirteenth-century English coronation liturgy, opens up a greater understanding of the survival or resurrection of Anglo-Saxon intellectual, spiritual and/or artistic impulses beyond the Norman Conquest.
In the other direction, increased appreciation for the philosophical connections between the Anglo-Saxons’ hitherto unexplained love for garnets and ancient and classical philosophy and science opens up avenues into questioning Roman continuity, international connections, and other topics in early Anglo-Saxon studies.
Through the interpretive possibilities presented by Plato’s ‘Timaeus’, we can begin to examine how philosophy through geometric allegories may have informed the aesthetics of status and social organisation through a very long period of history. This is a vast field that has only just been opened.
As we prepare for a coronation this year, on the Cosmati Pavement and according to long-observed ritual, we may reflect on what impact this art history (outlined only briefly in this article) has had upon the intervening centuries of English culture: what has evolved and how. I am preparing a book for publication this year, which has examined this later history in great depth, including moments of unexpectedly intense Anglo-Saxon artistic revival in places as diverse as the Tudor Soulton Hall in Shropshire, the works of Sir Christopher Wren, Newgate Prison, and government buildings in England and the USA.
The millefiori glass in the Staffordshire Hoard and Sutton Hoo combines with the Maldon holy water sprinkler and the Rhenish Helm roofs to cement the rhombic dodecahedron as a significant piece of intellectual freight that holds substantial explanatory power within Anglo-Saxon (and Frankish) art and architectural history. This fundamental form is naturally embodied in an explicit way by whole garnets, and in a symbolic (or occult) manner by use of this material.
Our new understanding of this geometry, and its central role in the meaning of thirteenth-century English coronation liturgy, opens up a greater understanding of the survival or resurrection of Anglo-Saxon intellectual, spiritual and/or artistic impulses beyond the Norman Conquest.
In the other direction, increased appreciation for the philosophical connections between the Anglo-Saxons’ hitherto unexplained love for garnets and ancient and classical philosophy and science opens up avenues into questioning Roman continuity, international connections, and other topics in early Anglo-Saxon studies.
Through the interpretive possibilities presented by Plato’s ‘Timaeus’, we can begin to examine how philosophy through geometric allegories may have informed the aesthetics of status and social organisation through a very long period of history. This is a vast field that has only just been opened.
As we prepare for a coronation this year, on the Cosmati Pavement and according to long-observed ritual, we may reflect on what impact this art history (outlined only briefly in this article) has had upon the intervening centuries of English culture: what has evolved and how. I am preparing a book for publication this year, which has examined this later history in great depth, including moments of unexpectedly intense Anglo-Saxon artistic revival in places as diverse as the Tudor Soulton Hall in Shropshire, the works of Sir Christopher Wren, Newgate Prison, and government buildings in England and the USA.
Acknowledgements
Rather than the work of one man, there are four ‘knights of the garnet’ with regard to this extraordinary journey of insight. My partner, James Syrett, made many critically important observations regarding the rhombic dodecahedron; Ædmund Thompson’s unrivalled knowledge of and inspired insight into Anglo-Saxon material culture and philosophy has contributed immensely; and Tim Ashton’s mastery of biographical history, encouragement and patronage of this project has likewise enabled the wider project to achieve success.
Additionally the Thegns of Mercia family as a whole has been immensely supportive during this period, and thanks also go to the many contacts in my network who have encouraged me and permitted access to resources and locations of importance in this research, both in terms of discovering things and ruling things out.
It would also be appropriate to again signal my thanks and respect to the university departments of my education years ago — to the Department of Anglo-Saxon, Norse and Celtic at the University of Cambridge, and The Centre for the Study of the Country House at Leicester University.
Additionally the Thegns of Mercia family as a whole has been immensely supportive during this period, and thanks also go to the many contacts in my network who have encouraged me and permitted access to resources and locations of importance in this research, both in terms of discovering things and ruling things out.
It would also be appropriate to again signal my thanks and respect to the university departments of my education years ago — to the Department of Anglo-Saxon, Norse and Celtic at the University of Cambridge, and The Centre for the Study of the Country House at Leicester University.
Resources
Blockley, K., ‘The Anglo-Saxon Churches of Canterbury Archaeologically Reconsidered’, PhD dissertation (Durham University, 2000), Available at Durham E-Theses Online: http://etheses.dur.ac.uk/4320/
Fern, C., T. Dickinson and L. Webster, eds., The Staffordshire Hoard: an Anglo-Saxon treasure (London, 2019)
Heath, T.L., trans. and ed., Euclid: the thirteen books of the elements (New York, 1956), 3 vols.
i Altet, X.B., The Early Middle Ages: from Late Antiquity to AD 1000 (Cologne, 2002)
Lee, D., trans. and ed., Plato: Timaeus and Critias (London, 1965)
Mortimer, P. ‘The riddle of the pyramids: An attempt to unravel their meaning. A typology and comments on chronology’. Mortimer, P. & Bunker, M. The sword in Anglo-Saxon England: from the 5th to 7th century (Ely, 2019)
Rodwell, W., and D.S. Neal, The Cosmatesque Mosaics of Westminster Abbey (Oxford, 2019)
Taylor, H.M. and J. Taylor, Anglo-Saxon Architecture (Cambridge, 1965), 2 vols.
Fern, C., T. Dickinson and L. Webster, eds., The Staffordshire Hoard: an Anglo-Saxon treasure (London, 2019)
Heath, T.L., trans. and ed., Euclid: the thirteen books of the elements (New York, 1956), 3 vols.
i Altet, X.B., The Early Middle Ages: from Late Antiquity to AD 1000 (Cologne, 2002)
Lee, D., trans. and ed., Plato: Timaeus and Critias (London, 1965)
Mortimer, P. ‘The riddle of the pyramids: An attempt to unravel their meaning. A typology and comments on chronology’. Mortimer, P. & Bunker, M. The sword in Anglo-Saxon England: from the 5th to 7th century (Ely, 2019)
Rodwell, W., and D.S. Neal, The Cosmatesque Mosaics of Westminster Abbey (Oxford, 2019)
Taylor, H.M. and J. Taylor, Anglo-Saxon Architecture (Cambridge, 1965), 2 vols.
Web resources
Archaeology Data Service, Staffordshire Hoard: archaeologydataservice.ac.uk/archives/view/staffshoard_he_2017
Fitzwilliam Museum, Cambridge: emc.fitzmuseum.cam.ac.uk
Portable Antiquities Scheme: finds.org.uk
Westminster Abbey: westminster-abbey.org
Archaeology Data Service, Staffordshire Hoard: archaeologydataservice.ac.uk/archives/view/staffshoard_he_2017
Fitzwilliam Museum, Cambridge: emc.fitzmuseum.cam.ac.uk
Portable Antiquities Scheme: finds.org.uk
- Clifford, T (2006) "SUSS-3C8EA4: A MEDIEVAL STAFF" Web page available at: https://finds.org.uk/database/artefacts/record/id/128035 [Accessed: 13 Apr 2023]
- Fittock, M (2019) "BH-692011: A ROMAN DODECAHEDRON" Web page available at: https://finds.org.uk/database/artefacts/record/id/941889 [Accessed: 13 Apr 2023]
- Maslin, S (2022) "SUR-A551E7: A EARLY MEDIEVAL PIN" Web page available at: https://finds.org.uk/database/artefacts/record/id/1084705 [Accessed: 13 Apr 2023]
- Rogerson, L (2022) "KENT-F499EE: A EARLY MEDIEVAL PIN" Web page available at: https://finds.org.uk/database/artefacts/record/id/1090156 [Accessed: 13 Apr 2023]
- Rivett, A (2022) "YORYM-F9D484: A EARLY MEDIEVAL PIN" Web page available at: https://finds.org.uk/database/artefacts/record/id/1088729 [Accessed: 13 Apr 2023]
- Scott, W (2011) "LEIC-15A132: A EARLY MEDIEVAL MOUNT" Web page available at: https://finds.org.uk/database/artefacts/record/id/467984 [Accessed: 13 Apr 2023]
Westminster Abbey: westminster-abbey.org
Further Information
Byrga Geniht: byrga.co.uk
Byrga Geniht on YouTube: youtube.com/@ByrgaGeniht
Forthcoming publication:
J.D. Wenn, Stones of the Magi: the history of magic in English stately architecture (London, expected 2023)
Byrga Geniht on YouTube: youtube.com/@ByrgaGeniht
Forthcoming publication:
J.D. Wenn, Stones of the Magi: the history of magic in English stately architecture (London, expected 2023)
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