Steriruncitruncated 5simplex
Steriruncitruncated 5simplex  

Rank  5 
Type  Uniform 
Notation  
Bowers style acronym  Captid 
Coxeter diagram  x3x3o3x3x () 
Elements  
Tera  30 truncated tetrahedral prisms, 20 hexagonal duoprisms, 12 prismatorhombated pentachora 
Cells  120 triangular prisms, 120+120 hexagonal prisms, 60 truncated tetrahedra, 30 cuboctahedra 
Faces  240 triangles, 90+180+360 squares, 240 hexagons 
Edges  360+720 
Vertices  360 
Vertex figure  Rectangular scalene, base edge lengths 1 and √2, remaining edge lengths √2 (5) and √3 (4) 
Measures (edge length 1)  
Circumradius  
Hypervolume  
Diteral angles  Tuttip–hip–hiddip: 135° 
Prip–tut–tuttip:  
Prip–hip–hiddip:  
Prip–trip–tuttip:  
Prip–co–prip:  
Central density  1 
Number of external pieces  62 
Level of complexity  40 
Related polytopes  
Army  Captid 
Regiment  Captid 
Dual  Rhombipyramidal pyramidal triacosihexecontateron 
Conjugate  None 
Abstract & topological properties  
Flag count  57600 
Euler characteristic  2 
Orientable  Yes 
Properties  
Symmetry  A_{5}×2, order 1440 
Convex  Yes 
Nature  Tame 
The steriruncitruncated 5simplex, also called the celliprismatotruncated hexateron, celliprismatotruncatododecateron, or captid, is a convex uniform 5polytope. It consists of 30 truncated tetrahedral prisms, 20 hexagonal duoprisms, and 12 prismatorhombated pentachora. 2 prismatorhombated pentachora, 2 truncated tetrahedral prisms, and 2 hexagonal duoprisms join at each vertex. As the name suggests, it is the steriruncitruncation of the 5simplex.
Vertex coordinates[edit  edit source]
The vertices of a steriruncitruncated 5simplex of edge length 1 can be given in 6 dimensions as all permutations of:
 .
Representations[edit  edit source]
A steriruncitruncated 5simplex has the following Coxeter diagrams:
 x3x3o3x3x () (full symmetry)
 xxxux3xxxoo3ooxxx3xuxxx&#xt (A_{4} axial, prismatorhombated pentachoronfirst)
Gallery[edit  edit source]

A_{4} orthographic projection

A_{3}

A_{2}
Related polytopes[edit  edit source]
The steriruncitruncated 5simplex is the colonel of a threemember regiment that also includes the retrocelliprismatotruncatododecateron and lepidocelliprismatotruncatododecateron.
External links[edit  edit source]
 Bowers, Jonathan. "Category 13: Prismatorhombates and Kin" (#844).
 Klitzing, Richard. "captid".
 Wikipedia contributors. "Steriruncitruncated 5simplex".