Stericantellated 5simplex
Stericantellated 5simplex  

Rank  5 
Type  Uniform 
Notation  
Bowers style acronym  Card 
Coxeter diagram  x3o3x3o3x () 
Elements  
Tera  20 triangular duoprisms, 30 cuboctahedral prisms, 12 small rhombated pentachora 
Cells  120+120 triangular prisms, 30 octahedra, 90 cubes, 60 cuboctahedra 
Faces  120+240 triangles, 180+360 squares 
Edges  360+360 
Vertices  180 
Vertex figure  Antiduowedge, edge lengths 1 (bases of disphenoid cell and top square) and √2 (remaining edges) 
Measures (edge length 1)  
Circumradius  
Hypervolume  
Diteral angles  Cope–trip–triddip: 135° 
Srip–co–cope:  
cope–cube–cope: 120°  
Srip–trip–cope:  
Srip–oct–srip:  
Central density  1 
Number of external pieces  62 
Level of complexity  28 
Related polytopes  
Army  Card 
Regiment  Card 
Dual  Anticupolanotched hecatonoctacontateron 
Conjugate  None 
Abstract & topological properties  
Flag count  40320 
Euler characteristic  2 
Orientable  Yes 
Properties  
Symmetry  A_{5}×2, order 1440 
Convex  Yes 
Nature  Tame 
The stericantellated 5simplex, also called the cellirhombated hexateron, cellirhombidodecateron, or card, is a convex uniform 5polytope. 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 5simplex.
Vertex coordinates[edit  edit source]
The vertices of a stericantellated 5simplex of edge length 1 can be given in 6 dimensions as all permutations of:
 .
Representations[edit  edit source]
A stericantellated 5simplex has the following Coxeter diagrams:
 x3o3x3o3x () (full symmetry)
 xxxo3xxoo3ooxx3oxxx&#xt (A_{4} axial, small rhombated pentachoronfirst)
 x(uo)(xd)(uo)x x(xx)(xo)(ou)x3o(xo)(xx)(xo)o3x(ou)(xo)(xx)x&#xt (A_{3}×A_{1} axial, cuboctahedral prismfirst)
Gallery[edit  edit source]

A_{4} orthographic projection

A_{3}

A_{2}
Related polytopes[edit  edit source]
The stericantellated 5simplex is the colonel of a regiment of 18 members. Of these, 9 have full symmetry, while the other 9 have single A_{5} symmetry only.
External links[edit  edit source]
 Klitzing, Richard. "card".
 Wikipedia contributors. "Stericantellated 5simplex".