Birectified 6simplex
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Birectified 6simplex  

Rank  6 
Type  Uniform 
Notation  
Bowers style acronym  Bril 
Coxeter diagram  o3o3x3o3o3o () 
Elements  
Peta  7 rectified 5simplices, 7 birectified 5simplices 
Tera  21 pentachora, 21+42 rectified pentachora 
Cells  35+105 tetrahedra, 105 octahedra 
Faces  140+210 triangles 
Edges  210 
Vertices  35 
Vertex figure  Triangulartetrahedral duoprism, edge length 1 
Measures (edge length 1)  
Circumradius  
Hypervolume  
Dipetal angles  Dot–rap–rix: 
Dot–rap–dot:  
Rix–pen–rix:  
Height  
Central density  1 
Number of external pieces  14 
Level of complexity  10 
Related polytopes  
Army  Bril 
Regiment  Bril 
Conjugate  None 
Abstract & topological properties  
Flag count  50400 
Euler characteristic  0 
Orientable  Yes 
Properties  
Symmetry  A_{6}, order 5040 
Flag orbits  10 
Convex  Yes 
Nature  Tame 
The birectified 6simplex (also called the birectified heptapteon or bril) is a convex uniform 6polytope. It has 7 rectified hexatera and 7 dodecatera as facets. 3 rectified hexatera and 4 dodecatera join at each triangulartetrahedral duoprismatic vertex. As the name suggests, it is the birectification of the 6simplex.
It is also a convex segmentotope, as a rectified hexateron atop dodecateron.
Vertex coordinates[edit  edit source]
The vertices of a birectified 6simplex of edge length 1 can be given in seven dimensions as all permutations of:
 .
Representations[edit  edit source]
A birectified 6simplex has the following Coxeter diagrams:
 o3o3x3o3o3o () (full symmetry)
 oo3xo3ox3oo3oo&#x (A_{5} axial, rectified hexateron atop dodecateron)
 oxo xoo3oxo3oox3ooo&#xt (A_{4}×A_{1} axial, pentachoronfirst)
 oxoo3ooxo oxoo3ooxo3ooox&#xt (A_{3}×A_{2} axial, vertexfirst)
Gallery[edit  edit source]

A_{5} orthographic projection

A_{4}

A_{3}

A_{2}
Related polytopes[edit  edit source]
The birectified 6simplex is the colonel of a regiment of 18 members.
External links[edit  edit source]
 Klitzing, Richard. "bril".
 Wikipedia contributors. "Birectified 6simplex".