Bitruncated 5-simplex

Bitruncated 5-simplex
(OFF file)
Rank	5
Type	Uniform
Notation
Bowers style acronym	Bittix
Coxeter diagram	o3x3x3o3o ()
Elements
Tera	6 truncated pentachora, 6 decachora
Cells	15 tetrahedra, 15+30 truncated tetrahedra
Faces	20+60 triangles, 60 hexagons
Edges	60+90
Vertices	60
Vertex figure	Triangular scalene, edge lengths 1 (base triangle and top edge) and √3 (sides)
Measures (edge length 1)
Circumradius	${\frac {\sqrt {87}}{6}}\approx 1.55456$
Hypervolume	${\frac {841{\sqrt {3}}}{240}}\approx 6.06939$
Diteral angles	Deca–tut–tip: $\arccos \left(-{\frac {1}{5}}\right)\approx 101.53696^{\circ }$
	Tip–tet–tip: $\arccos \left({\frac {1}{5}}\right)\approx 78.46304^{\circ }$
	Deca–tut–deca: $\arccos \left({\frac {1}{5}}\right)\approx 78.46304^{\circ }$
Central density	1
Number of external pieces	12
Level of complexity	10
Related polytopes
Army	Bittix
Regiment	Bittix
Dual	Triangular-scalenic hexecontateron
Conjugate	None
Abstract & topological properties
Flag count	7200
Euler characteristic	2
Orientable	Yes
Properties
Symmetry	A5, order 720
Convex	Yes
Nature	Tame

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:

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

Representations

A bitruncated 5-simplex has the following Coxeter diagrams:

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

Gallery

• 

  A₄ orthographic projection

• 

  A₃

• 

  A₂

External links

• Bowers, Jonathan. "Category 2: Truncates" (#21).

• Klitzing, Richard. "bittix".
• Wikipedia contributors. "Bitruncated 5-simplex".