Bitruncated 5-simplex

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Bitruncated 5-simplex
Rank5
TypeUniform
Notation
Bowers style acronymBittix
Coxeter diagramo3x3x3o3o ()
Elements
Tera6 truncated pentachora, 6 decachora
Cells15 tetrahedra, 15+30 truncated tetrahedra
Faces20+60 triangles, 60 hexagons
Edges60+90
Vertices60
Vertex figureTriangular scalene, edge lengths 1 (base triangle and top edge) and 3 (sides)
Measures (edge length 1)
Circumradius
Hypervolume
Diteral anglesDeca–tut–tip:
 Tip–tet–tip:
 Deca–tut–deca:
Central density1
Number of external pieces12
Level of complexity10
Related polytopes
ArmyBittix
RegimentBittix
DualTriangular-scalenic hexecontateron
ConjugateNone
Abstract & topological properties
Flag count7200
Euler characteristic2
OrientableYes
Properties
SymmetryA5, order 720
Flag orbits10
ConvexYes
NatureTame

The bitruncated 5-simplex, also called the bitruncated hexateron or bittix, is a convex uniform 5-polytope. It consists of 6 truncated pentachora and 6 decachora. 2 truncated pentachora and 3 decachora join at each vertex. As the name suggests, it is the bitruncation of the 5-simplex.

Vertex coordinates[edit | edit source]

The vertices of a bitruncated 5-simplex of edge length 1 can be given in 6 dimensions as all permutations of:

  • .

Representations[edit | edit source]

A bitruncated 5-simplex has the following Coxeter diagrams:

  • o3x3x3o3o () (full symmetry)
  • oox3xux3xoo3ooo&#xt (A4 axial, decachoron-first)

Gallery[edit | edit source]

External links[edit | edit source]