Stericated 5simplex
(Redirected from Small cellidodecateron)
Stericated 5simplex  

Rank  5 
Type  Uniform 
Notation  
Bowers style acronym  Scad 
Coxeter diagram  x3o3o3o3x () 
Elements  
Tera  12 pentachora, 30 tetrahedral prisms, 20 triangular duoprisms 
Cells  60 tetrahedra, 120 triangular prisms 
Faces  120 triangles, 90 squares 
Edges  120 
Vertices  30 
Vertex figure  Tetrahedral antiprism, edge lengths 1 (base) and √2 (sides) 
Measures (edge length 1)  
Circumradius  1 
Hypervolume  
Diteral angles  Tepe–trip–triddip: 135° 
Pen–tet–tepe:  
Central density  1 
Number of external pieces  62 
Level of complexity  8 
Related polytopes  
Army  Scad 
Regiment  Scad 
Dual  Tetrahedralantitegmatic triacontateron 
Conjugate  None 
Abstract & topological properties  
Flag count  11520 
Euler characteristic  2 
Orientable  Yes 
Properties  
Symmetry  A_{5}×2, order 1440 
Convex  Yes 
Nature  Tame 
The stericated 5simplex, also called the small cellated hexateron, small cellidodecateron, or scad, is a convex uniform 5polytope. It consists of 12 regular pentachora, 30 tetrahedral prisms, and 20 triangular duoprisms. 2 pentachora, 8 tetrahedral prisms, and 6 triangular duoprisms join at each vertex. It can be formed by expanding the facets of the 5simplex outward.
Vertex coordinates[edit  edit source]
The vertices of a stericated 5simplex of edge length 1 can be given in 6 dimensions as all permutations of:
 .
Representations[edit  edit source]
A stericated 5simplex has the following Coxeter diagrams:
 x3o3o3o3x () (full symmetry)
 xxo3ooo3ooo3oxx&#xt (A_{4} axial, pentachoronfirst)
 x(xo)o3o(xo)x x(ox)o3o(ox)x&#xt (A_{2}×A_{2} axial, triangular duoprismfirst)
 x(uo)x x(ox)o3o(oo)o3o(ox)x&#xt (A_{3}×A_{1} axial, tetrahedral prismfirst)
Gallery[edit  edit source]

A_{4} orthographic projection

A_{3}

A_{2}
Related polytopes[edit  edit source]
The stericated 5simplex is the colonel of a regiment with 11 members. Of these 11, 7 have full symmetry, while the other 4 have single A_{5} symmetry only.
External links[edit  edit source]
 Bowers, Jonathan. "Category 9: Podiumverts" (#681).
 Klitzing, Richard. "scad".
 Wikipedia contributors. "Stericated 5simplex".