Pentitruncated 6simplex
Pentitruncated 6simplex  

Rank  6 
Type  Uniform 
Notation  
Bowers style acronym  Tocal 
Coxeter diagram  x3x3o3o3o3x () 
Elements  
Peta  21 pentachoric prisms 35 hexagonaltetrahedral duoprisms 7 truncated 5simplices 7 stericated 5simplices 35 triangulartruncated tetrahedral duoprisms 21 truncated pentachoric prisms 
Tera  42+42 pentachora 105+105+105 tetrahedral prisms 140 triangular duoprisms 140 triangularhexagonal duoprisms 42 truncated pentachora 105 truncated tetrahedral prisms 
Cells  210+210 tetrahedra 210+420+420 triangular prisms 210 hexagonal prisms 105 truncated tetrahedra 
Faces  420+420 triangles 210+630 squares 140 hexagons 
Edges  105+420+420 
Vertices  210 
Vertex figure  Skew tetrahedral antiprismatic pyramid, edge lengths 1 (base tetrahedra), √2 (sides of antiprism and lacings to one base), and √3 (lacings to other base) 
Measures (edge length 1)  
Circumradius  
Hypervolume  
Dipetal angles  Tratut–thiddip–hatet: 
Penp–tepe–hatet:  
Tippip–tuttip–tratut:  
Scad–pen–penp:  
Tix–tip–tippip:  
Scad–tepe–hatet:  
Scad–triddip–tratut:  
Scad–tepe–tippip:  
Central density  1 
Number of external pieces  126 
Level of complexity  96 
Related polytopes  
Army  Tocal 
Regiment  Tocal 
Conjugate  None 
Abstract & topological properties  
Flag count  483840 
Euler characteristic  0 
Orientable  Yes 
Properties  
Symmetry  A_{6}, order 5040 
Convex  Yes 
Nature  Tame 
The pentitruncated 6simplex, also called the pentitruncated heptapeton, tericellated heptapeton, or tocal, is a convex uniform 6polytope. It consists of 7 truncated 5simplices, 7 stericated 5simplices, 21 pentachoric prisms, 21 truncated pentachoric prisms, 35 hexagonaltetrahedral duoprisms, and 35 triangulartruncated tetrahedral duoprisms. 1 truncated 5simplex, 1 stericated 5simplex, 1 pentachoric prism, 4 truncated pentachoric prisms, 4 hexagonaltetrahedral duoprisms, and 6 triangulartruncated tetrahedral duoprisms join at each vertex. As the name suggests, it is the pentitruncation 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 pentitruncated 6simplex of edge length 1 can be given in 7 dimensions as all permutations of:
 .
Related polytopes[edit  edit source]
The pentitruncated 6simplex is the colonel of a regiment that includes 15 uniform members.
External links[edit  edit source]
 Klitzing, Richard. "tocal".
 Wikipedia contributors. "Pentitruncated 6simplex".