Stericantellated 5-simplex

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Stericantellated 5-simplex
Rank5
TypeUniform
Notation
Bowers style acronymCard
Coxeter diagramx3o3x3o3x ()
Elements
Tera20 triangular duoprisms, 30 cuboctahedral prisms, 12 small rhombated pentachora
Cells120+120 triangular prisms, 30 octahedra, 90 cubes, 60 cuboctahedra
Faces120+240 triangles, 180+360 squares
Edges360+360
Vertices180
Vertex figureAntiduowedge, edge lengths 1 (bases of disphenoid cell and top square) and 2 (remaining edges)
Measures (edge length 1)
Circumradius
Hypervolume
Diteral anglesCope–trip–triddip: 135°
 Srip–co–cope:
 cope–cube–cope: 120°
 Srip–trip–cope:
 Srip–oct–srip:
Central density1
Number of external pieces62
Level of complexity28
Related polytopes
ArmyCard
RegimentCard
DualAnticupolanotched hecatonoctacontateron
ConjugateNone
Abstract & topological properties
Flag count40320
Euler characteristic2
OrientableYes
Properties
SymmetryA5×2, order 1440
ConvexYes
NatureTame

The stericantellated 5-simplex, also called the cellirhombated hexateron, cellirhombidodecateron, or card, is a convex uniform 5-polytope. It consists of 20 triangular duoprisms, 30 cuboctahedral prisms, and 12 small rhombated pentachora. 1 triangular duoprism, 2 small rhombated pentachora, and 4 cuboctahedral prisms join at each vertex. As the name suggests, it is the stericantellation of the 5-simplex.

Vertex coordinates[edit | edit source]

The vertices of a stericantellated 5-simplex of edge length 1 can be given in 6 dimensions as all permutations of:

  • .

Representations[edit | edit source]

A stericantellated 5-simplex has the following Coxeter diagrams:

  • x3o3x3o3x () (full symmetry)
  • xxxo3xxoo3ooxx3oxxx&#xt (A4 axial, small rhombated pentachoron-first)
  • x(uo)(xd)(uo)x x(xx)(xo)(ou)x3o(xo)(xx)(xo)o3x(ou)(xo)(xx)x&#xt (A3×A1 axial, cuboctahedral prism-first)

Gallery[edit | edit source]

Related polytopes[edit | edit source]

The stericantellated 5-simplex is the colonel of a regiment of 18 members. Of these, 9 have full symmetry, while the other 9 have single A5 symmetry only.

External links[edit | edit source]