Bitruncated 6-simplex

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Bitruncated 6-simplex
Rank6
TypeUniform
Notation
Bowers style acronymBatal
Coxeter diagramo3x3x3o3o3o ()
Elements
Peta7 truncated hexatera, 7 bitruncated hexatera
Tera21 pentachora, 42 truncated pentachora, 21 decachora
Cells105 tetrahedra, 35+105 truncated tetrahedra
Faces35+210 triangles, 140 hexagons
Edges105+210
Vertices105
Vertex figureTetrahedral scalene , edge lengths 1 (base tetrahedron and top edge) and 3 (sides)
Measures (edge length 1)
Circumradius
Hypervolume
Dipetal anglesTix-tip-bittix:
 Bittix-deca-bittix:
 Tix-pen-tix:
Central density1
Number of external pieces14
Level of complexity15
Related polytopes
ArmyBatal
RegimentBatal
ConjugateNone
Abstract & topological properties
Flag count75600
Euler characteristic0
OrientableYes
Properties
SymmetryA6, order 5040
ConvexYes
NatureTame

The bitruncated 6-simplex (also called the bitruncated heptapeton or batal) is a convex uniform 6-polytope. It consists of 7 truncated hexatera and 7 bitruncated hexatera as facets. 2 truncated hexatera and 4 bitruncated hexatera join at each vertex. As the name suggests, it is the bitruncation of the 6-simplex.

Vertex coordinates[edit | edit source]

The vertices of a bitruncated 6-simplex of edge length 1 can be given in seven dimensions as all permutations of:

  • .

Representations[edit | edit source]

A bitruncated 6-simplex has the following Coxeter diagrams:

  • o3x3x3o3o3o () (full symmetry)
  • xoo3xux3oox3ooo3ooo&#xt (A5 axial, truncated hexateron-first)

Gallery[edit | edit source]

External links[edit | edit source]