Runcitruncated 5simplex
The runcitruncated 5simplex, also called the prismatotruncated hexateron or pattix, is a convex uniform 5polytope. It consists of 15 octahedral prisms, 20 triangularhexagonal duoprisms, 6 small rhombated pentachora, and 6 prismatorhombated pentachora. One small rhombated pentachoron, 1 octahedral prism, 2 prismatorhombated pentachora, and 2 triangularhexagonal duoprisms join at each vertex. As the name suggests, it is the runcitruncation of the 5simplex.
Runcitruncated 5simplex  

Rank  5 
Type  Uniform 
Notation  
Bowers style acronym  Pattix 
Coxeter diagram  x3x3o3x3o () 
Elements  
Tera  15 octahedral prisms, 20 triangularhexagonal duoprisms, 6 small rhombated pentachora, 6 prismatorhombated pentachora 
Cells  60+60+60 triangular prisms, 30 octahedra, 60 hexagonal prisms, 15 truncated tetrahedra, 30 cuboctahedra 
Faces  60+120+120 triangles, 180+180 squares, 60 hexagons 
Edges  90+180+360 
Vertices  180 
Vertex figure  Wedge pyramid, edge lengths 1 (base square and top edge of wedge), √2 (sides of wedge and lacings to square), and √3 (lacings to top edge) 
Measures (edge length 1)  
Circumradius  
Hypervolume  
Diteral angles  Ope–trip–thiddip: 135° 
Srip–oct–ope:  
Srip–trip–thiddip:  
Prip–hip–thiddip:  
Prip–trip–ope:  
Prip–co–srip:  
Prip–tut–prip:  
Central density  1 
Number of external pieces  47 
Level of complexity  45 
Related polytopes  
Army  Pattix 
Regiment  Pattix 
Dual  Notchpyramidal hecatonoctacontateron 
Conjugate  None 
Abstract & topological properties  
Flag count  32400 
Euler characteristic  2 
Orientable  Yes 
Properties  
Symmetry  A_{5}, order 720 
Convex  Yes 
Nature  Tame 
Vertex coordinates edit
The vertices of a runcitruncated 5simplex of edge length 1 can be given in 6 dimensions as all permutations of:
 .
Representations edit
A runcitruncated 5simplex has the following Coxeter diagrams:
 x3x3o3x3o ( ) (full symmetry)
 xuxx3ooxx3xxxo3ooox&#xt (A_{4} axial, small rhombated pentachoronfirst)
Gallery edit

A_{4} orthographic projection

A_{3}

A_{2}
Related polytopes edit
The runcitruncated 5simplex is the colonel of a regiment of 7 members.
External links edit
 Klitzing, Richard. "pattix".
 Wikipedia contributors. "Runcitruncated 5simplex".