Small birhombidodecateron

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Small birhombidodecateron
5-simplex t13.svg
Rank5
TypeUniform
SpaceSpherical
Notation
Bowers style acronymSibrid
Coxeter diagramo3x3o3x3o (CDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png)
Elements
Tera20 triangular duoprisms, 12 small rhombated pentachora
Cells120 triangular prisms, 30 octahedra, 30 cuboctahedra
Faces120+120 triangles, 180 squares
Edges360
Vertices90
Vertex figureTetragonal disphenoidal prism, edge lengths 1 (base squares) and 2 (sides) Bicantellated 5-simplex verf.png
Measures (edge length 1)
Circumradius
Hypervolume
Diteral anglesSrip–trip–triddip:
 Srip–co–srip:
 Srip–oct–srip:
Central density1
Number of external pieces32
Level of complexity12
Related polytopes
ArmySibrid
RegimentSibrid
DualDisphenoidal tegmatic enneacontateron
ConjugateNone
Abstract & topological properties
Euler characteristic2
OrientableYes
Properties
SymmetryA5×2, order 1440
ConvexYes
NatureTame

The small birhombidodecateron, or sibrid, also called the small birhombated hexateron or bicantellated 5-simplex, is a convex uniform polyteron. It consists of 20 triangular duoprisms and 12 small rhombated pentachora. 2 triangular duoprisms and 4 small rhombated pentachora join at each vertex. As the name suggests, it is the bicantellation of the hexateron. It is also the rectified dodecateron.

Vertex coordinates[edit | edit source]

The vertices of a small birhombidodecateron of edge length 1 can be given in 6 dimensions as all permutations of:

Representations[edit | edit source]

A small birhombidodecateron has the following Coxeter diagrams:

  • o3x3o3x3o (full symmetry)
  • xoo3oxx3xxo3oox&#xt (A4 axial, small rhombated pentachoron-first)

Gallery[edit | edit source]

Related polytopes[edit | edit source]

The regiment of the small birhombidodecateron includes a total of 23 members. Of these, 15 have full symmetry, while the remaining 8 have single A5 symmetry only.

o3o3o3o3o truncations
Name OBSA CD diagram Picture
Hexateron hix CDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
5-simplex t0.svg
Rectified hexateron rix CDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
5-simplex t1.svg
Dodecateron dot CDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
5-simplex t2.svg
Rectified hexateron rix CDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
5-simplex t1.svg
Hexateron hix CDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
5-simplex t0.svg
Truncated hexateron tix CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
5-simplex t01.svg
Bitruncated hexateron bittix CDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
5-simplex t12.svg
Bitruncated hexateron bittix CDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
5-simplex t12.svg
Truncated hexateron tix CDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
5-simplex t01.svg
Small rhombated hexateron sarx CDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
5-simplex t02.svg
Small birhombidodecateron sibrid CDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
5-simplex t13.svg
Small rhombated hexateron sarx CDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
5-simplex t02.svg
Great rhombated hexateron garx CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
5-simplex t012.svg
Great birhombidodecateron gibrid CDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
5-simplex t123.svg
Great rhombated hexateron garx CDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
5-simplex t012.svg
Small prismated hexateron spix CDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
5-simplex t03.svg
Small prismated hexateron spix CDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
5-simplex t03.svg
Prismatotruncated hexateron pattix CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
5-simplex t013.svg
Prismatorhombated hexateron pirx CDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
5-simplex t023.svg
Prismatorhombated hexateron pirx CDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
5-simplex t023.svg
Prismatotruncated hexateron pattix CDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
5-simplex t013.svg
Great prismated hexateron gippix CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
5-simplex t0123.svg
Great prismated hexateron gippix CDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
5-simplex t0123.svg
Small cellidodecateron scad CDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
5-simplex t04.svg
Celliprismated hexateron cappix CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
5-simplex t014.svg
Cellirhombidodecateron card CDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
5-simplex t024.svg
Celligreatorhombated hexateron cograx CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
5-simplex t0124.svg
Celliprismated hexateron cappix CDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
5-simplex t014.svg
Celliprismatotruncatododecateron captid CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
5-simplex t0134.svg
Celligreatorhombated hexateron cograx CDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
5-simplex t0124.svg
Great cellidodecateron gocad CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
5-simplex t01234.svg

External links[edit | edit source]