# Bitruncated 5-simplex

(Redirected from Bitruncated hexateron)
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${\displaystyle {\frac {\sqrt {87}}{6}}\approx 1.55456}$
Hypervolume${\displaystyle {\frac {841{\sqrt {3}}}{240}}\approx 6.06939}$
Diteral anglesDeca–tut–tip: ${\displaystyle \arccos \left(-{\frac {1}{5}}\right)\approx 101.53696^{\circ }}$
Tip–tet–tip: ${\displaystyle \arccos \left({\frac {1}{5}}\right)\approx 78.46304^{\circ }}$
Deca–tut–deca: ${\displaystyle \arccos \left({\frac {1}{5}}\right)\approx 78.46304^{\circ }}$
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
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

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

• ${\displaystyle \left({\sqrt {2}},\,{\sqrt {2}},\,{\frac {\sqrt {2}}{2}},\,0,\,0,\,0\right)}$.

## Representations

A bitruncated 5-simplex has the following Coxeter diagrams:

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