Small birhombipenteractitriacontaditeron

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Small birhombipenteractitriacontaditeron
5-cube t13.svg
Rank5
TypeUniform
SpaceSpherical
Notation
Bowers style acronymSibrant
Coxeter diagramo4x3o3x3o (CDel node.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png)
Elements
Tera80 triangular-square duoprisms, 32 small rhombated pentachora, 10 rectified icositetrachora
Cells320 triangular prisms, 80 octahedra, 240 cubes, 40+160 cuboctahedra
Faces320+320+320 triangles, 240+960 squares
Edges960+960
Vertices480
Vertex figureDigonal disphenoidal prism, edge lengths 1 (base square and two edges of rectangle base) and 2 (sides and other edges of base rectangle) Bicantellated penteract verf.png
Measures (edge length 1)
Circumradius
Hypervolume
Diteral anglesRico–cube–tisdip:
 Srip–trip–tisdip:
 Srip–oct–srip:
 Rico–co–srip:
 Rico–co–rico: 90°
Central density1
Number of external pieces122
Level of complexity24
Related polytopes
ArmySibrant
RegimentSibrant
DualDisphenoidal tegmatic tetracosioctacontateron
ConjugateNone
Abstract & topological properties
Flag count92160
Euler characteristic2
OrientableYes
Properties
SymmetryB5, order 3840
ConvexYes
NatureTame

The small birhombipenteractitriacontaditeron or sibrant, also called the bicantellated 5-cube, is a convex uniform polyteron. It consists of 80 triangular-square duoprisms, 32 small rhombated pentachora, and 10 rectified icositetrachora. 2 triangular-square duoprisms, 2 small rhombated pentachora, and 2 rectified icositetrachora join at each vertex. As the name suggests, it is the bicantellation of the penteract, or equivalenty of its dual triacontaditeron.

Vertex coordinates[edit | edit source]

The vertices of a small birhombipenteractitriacontaditeron of edge length 1 are given by all permutations of:

Representations[edit | edit source]

A small birhombipenteractitriacontaditeron has the following Coxeter diagrams:

  • o4x3o3x3o (full symmetry)
  • x3o3x *b3x3o (CDel nodes 11.pngCDel split2.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png) (D5 symmetry, as cantellated demipenteract)
  • s4x3o3x3o (CDel node h.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png) (D5 symmetry, as alternated faceting)
  • ooqoo4xxoxx3oxxxo3xooox&#xt (B4 axial, rectified icositetrachoron-first)

Gallery[edit | edit source]

Related polytopes[edit | edit source]

The regiment of the small birhombipenteractitriacontaditeron includes a total of 47 members. Of these, 31 have full symetry, while the remaining 16 have D5 symmetry only.

o4o3o3o3o truncations
Name OBSA CD diagram Picture
Penteract pent CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
5-cube t0.svg
Rectified penteract rin CDel node.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
5-cube t1.svg
Penteractitriacontaditeron nit CDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
5-cube t2.svg
Rectified triacontaditeron rat CDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
5-cube t3.svg
Triacontaditeron tac CDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
5-cube t4.svg
Truncated penteract tan CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
5-cube t01.svg
Bitruncated penteract bittin CDel node.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
5-cube t12.svg
Bitruncated triacontaditeron bittit CDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
5-cube t23.svg
Truncated triacontaditeron tot CDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
5-cube t34.svg
Small rhombated penteract sirn CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
5-cube t02.svg
Small birhombated penteract sibrant CDel node.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
5-cube t13.svg
Small rhombated triacontaditeron sart CDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
5-cube t24.svg
Great rhombated penteract girn CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.png
5-cube t012.svg
Great birhombated penteract gibrant CDel node.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
5-cube t123.svg
Great rhombated triacontaditeron gart CDel node.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
5-cube t234.svg
Small prismated penteract span CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
5-cube t03.svg
Small prismated triacontaditeron spat CDel node.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
5-cube t14.svg
Prismatotruncated penteract pattin CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
5-cube t013.svg
Prismatorhombated triacontaditeron pirt CDel node.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
5-cube t124.svg
Prismatorhombated penteract prin CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
5-cube t023.svg
Prismatotruncated triacontaditeron pattit CDel node.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
5-cube t134.svg
Great prismated penteract gippin CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
5-cube t0123.svg
Great prismated triacontaditeron gippit CDel node.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
5-cube t1234.svg
Small cellated penteract scant CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
5-cube t04.svg
Celliprismated triacontaditeron capt CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
5-cube t014.svg
Cellirhombated penteract carnit CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
5-cube t024.svg
Celligreatorhombated penteract cogrin CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.png
5-cube t0124.svg
Celliprismated penteract cappin CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
5-cube t034.svg
Celliprismatotruncated penteract captint CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
5-cube t0134.svg
Celligreatorhombated triacontaditeron cogart CDel node 1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
5-cube t0234.svg
Great cellated penteract gacnet CDel node 1.pngCDel 4.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node 1.png
5-cube t01234.svg

External links[edit | edit source]