Bitruncated 7-simplex

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Bitruncated 7-simplex
Rank7
TypeUniform
Notation
Bowers style acronymBittoc
Coxeter diagramo3x3x3o3o3o3o ()
Elements
Exa8 truncated heptapeta, 8 bitruncated heptapeta
Peta28 hexatera, 56 truncated hexatera, 28 bitruncated hexatera
Tera168 pentachora, 168 truncated pentachora, 56 decachora
Cells420 tetrahedra, 70+280 truncated tetrahedra
Faces56+560 triangles, 280 hexagons
Edges168+420
Vertices168
Vertex figurePentachoric scalene, edge lengths 1 (base and top edge) and 3 (sides)
Measures (edge length 1)
Circumradius
Hypervolume
Diexal anglesBatal–tix–til:
 Batal–bittix–batal:
 Til–hix–til:
Central density1
Number of external pieces16
Level of complexity21
Related polytopes
ArmyBittoc
RegimentBittoc
ConjugateNone
Abstract & topological properties
Flag count846720
Euler characteristic2
OrientableYes
Properties
SymmetryA7, order 40320
ConvexYes
NatureTame

The bitruncated octaexon, or bittoc, also called the bitruncated 7-simplex, is a convex uniform polyexon. It consists of 8 truncated heptapeta and 8 bitruncated heptapeta. 2 truncated heptapeta and 5 bitruncated heptapeta join at each vertex. As the name suggests, it is the bitruncation of the octaexon.

Vertex coordinates[edit | edit source]

The vertices of a bitruncated octaexon of edge length 1 can be given in eight dimensions as all permutations of:

External links[edit | edit source]

[[Category:A7 symmetry