Bicantellated 5-cube

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Bicantellated 5-cube
Rank5
TypeUniform
Notation
Bowers style acronymSibrant
Coxeter diagramo4x3o3x3o ()
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)
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 bicantellated 5-cube, also called the small birhombipenteractitriacontaditeron or sibrant, is a convex uniform 5-polytope. 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 5-cube, or equivalently of its dual 5-orthoplex.

Vertex coordinates[edit | edit source]

The vertices of a bicantellated 5-cube of edge length 1 are given by all permutations of:

  • .

Representations[edit | edit source]

A bicantellated 5-cube has the following Coxeter diagrams:

  • o4x3o3x3o () (full symmetry)
  • x3o3x3o *b3x () (D5 symmetry, as cantellated demipenteract)
  • s4x3o3x3o () (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 bicantellated 5-cube includes a total of 47 members. Of these, 31 have full symetry, while the remaining 16 have D5 symmetry only.

External links[edit | edit source]