Stericantellated 6simplex
Stericantellated 6simplex  

Rank  6 
Type  Uniform 
Notation  
Bowers style acronym  Cral 
Coxeter diagram  x3o3x3o3x3o () 
Elements  
Peta  35 triangularoctahedral duoprisms, 35 triangularcuboctahedral duoprisms, 21 small rhombated pentachoric prisms, 7 small birhombidodecatera, 7 cellirhombidodecatera 
Tera  140+140+140 triangular duoprisms, 210 triangularsquare duoprisms, 105 octahedral prisms, 105+105 cuboctahedral prisms, 21+42+42 small rhombated pentachora 
Cells  210+420+420+420+420+420 triangular prisms, 105+105 octahedra, 630 cubes, 105+210 cuboctahedra 
Faces  210+420+420+420+420 triangles, 630+1260+1260 squares 
Edges  630+1260+1260 
Vertices  630 
Vertex figure  Irregular edgediminished tetrahedral antifastegium, edge lengths 1 (base squares and top edge) and √2 (lacing edges) 
Measures (edge length 1)  
Circumradius  
Hypervolume  
Dipetal angles  Troct–triddip–traco: 
Srippip–cope–traco:  
Srippip–ope–troct:  
Sibrid–srip–srippip:  
Srippip–tisdip–traco:  
Sibrid–triddip–traco:  
Card–triddip–troct:  
Card–cope–srippip:  
Central density  1 
Number of external pieces  105 
Level of complexity  185 
Related polytopes  
Army  Cral 
Regiment  Cral 
Conjugate  None 
Abstract & topological properties  
Flag count  932400 
Euler characteristic  0 
Orientable  Yes 
Properties  
Symmetry  A_{6}, order 5040 
Convex  Yes 
Nature  Tame 
The stericantellated 6simplex, also called the stericantellated heptapeton, cellirhombated heptapeton, or cral, is a convex uniform 6polytope. It consists of 7 stericantellated 5simplices, 7 bicantellated 5simplices, 21 small rhombated pentachoric prisms, 21 triangularoctahedral duoprisms, and 35 triangularcuboctahedral duoprisms. 2 stericantellated 5simplices, 1 bicantellated 5simplex, 2 small rhombated pentachoric prisms, 1 triangularoctahedral duoprism, and 2 triangularcuboctahedral duoprisms join at each vertex. As the name suggests, it is the stericantellation of the 6simplex.
Gallery[edit  edit source]

A_{5} orthographic projection

A_{4}

A_{3}

A_{2}
Vertex coordinates[edit  edit source]
The vertices of a stericantellated 6simplex of edge length 1 can be given in 7 dimensions as all permutations of:
 .
Related polytopes[edit  edit source]
The regiment of the cellirhombated heptapeton contains 75 uniform members.
External links[edit  edit source]
 Klitzing, Richard. "cral".
 Wikipedia contributors. "Stericantellated 6simplex".
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