Steritruncated 5simplex
Steritruncated 5simplex  

Rank  5 
Type  Uniform 
Notation  
Bowers style acronym  Cappix 
Coxeter diagram  x3x3o3o3x () 
Elements  
Tera  15 tetrahedral prisms, 20 triangularhexagonal duoprisms, 6 truncated pentachora, 15 truncated tetrahedral prisms, 6 small prismatodecachora 
Cells  30+30 tetrahedra, 60+60+60 triangular prisms, 60 hexagonal prisms, 30 truncated tetrahedra 
Faces  120+120 triangles, 90+180 squares, 60 hexagons 
Edges  60+180+180 
Vertices  120 
Vertex figure  Skew triangular antiprismatic pyramid, edge lengths 1 (base triangles), √2 (sides of antiprism and lacings to one base), and √3 (lacings to other base) 
Measures (edge length 1)  
Circumradius  
Hypervolume  
Diteral angles  Tuttip–hip–thiddip: 135° 
Tepe–trip–thiddip: 135°  
Tip–tut–tuttip:  
Spid–tet–tepe:  
Spid–trip–thiddip:  
Spid–trip–tuttip:  
Spid–tet–tip:  
Central density  1 
Number of external pieces  62 
Level of complexity  40 
Related polytopes  
Army  Cappix 
Regiment  Cappix 
Dual  Triangularantitegmatic pyramidal hecatonicosateron 
Conjugate  None 
Abstract & topological properties  
Flag count  28800 
Euler characteristic  2 
Orientable  Yes 
Properties  
Symmetry  A_{5}, order 720 
Convex  Yes 
Nature  Tame 
The steritruncated 5simplex, also called the celliprismated hexateron or cappix, is a convex uniform 5polytope. It consists of 15 tetrahedral prisms, 20 triangularhexagonal duoprisms, 15 truncated tetrahedral prisms, 6 truncated pentachora, and 6 small prismatodecachora. One small prismatodecachoron, 1 tetrahedral prism, 1 truncated pentachoron, 3 truncated tetrahedral prisms, and 3 triangularhexagonal duoprisms join at each vertex. As the name suggests, it is the steritruncation of the 5simplex.
Vertex coordinates[edit  edit source]
The vertices of a steritruncated 5simplex of edge length 1 can be given in 6 dimensions as all permutations of:
 .
Representations[edit  edit source]
A steritruncated 5simplex has the following Coxeter diagrams:
 x3x3o3o3x () (full symmetry)
 xuxx3ooxx3oooo3xxxo&#xt (A_{4} axial, small prismatodecachoronfirst)
Gallery[edit  edit source]

A_{4} orthographic projection

A_{3}

A_{2}
Related polytopes[edit  edit source]
The steritruncated 5simplex is the colonel of a regiment of 7 members.
External links[edit  edit source]
 Klitzing, Richard. "cappix".
 Wikipedia contributors. "Steritruncated 5simplex".