Tritruncated 6-simplex

Tritruncated 6-simplex
(OFF file)
Rank	6
Type	Uniform
Notation
Bowers style acronym	Fe
Coxeter diagram	o3o3x3x3o3o ()
Elements
Peta	14 bitruncated hexatera
Tera	42 truncated pentachora, 42 decachora
Cells	70 tetrahedra, 210 truncated tetrahedra
Faces	280 triangles, 210 hexagons
Edges	420
Vertices	140
Vertex figure	Triangular disphenoid, edge lengths 1 (base triangles) and √3 (sides)
Measures (edge length 1)
Circumradius	${\sqrt {3}}\approx 1.73205$
Inradius	${\frac {\sqrt {21}}{6}}\approx 0.76376$
Hypervolume	${\frac {5887{\sqrt {7}}}{1440}}\approx 10.81635$
Dipetal angles	Bittix-deca-bittix: $\arccos \left(-{\frac {1}{6}}\right)\approx 99.59407^{\circ }$
	Bittix-tip-bittix: $\arccos \left({\frac {1}{6}}\right)\approx 80.40593^{\circ }$
Central density	1
Number of external pieces	14
Level of complexity	10
Related polytopes
Army	Fe
Regiment	Fe
Dual	Bitetradecapeton
Conjugate	None
Abstract & topological properties
Flag count	100800
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	A6×2, order 10080
Convex	Yes
Nature	Tame

The tritruncated 6-simplex (also the tritruncated heptapeton, tetradecapeton, or fe) is a convex noble uniform 6-polypetope. It consists of 14 bitruncated hexatera, with 6 joining at each vertex. As the name suggests, it is the tritruncation of the 6-simplex. It is the medial stage of truncations between the 6-simplex and its dual 6-simplex. It is also the medial vertex-first cross-section of the hepteract. It is also the 14-3-5 gyropeton.

Vertex coordinates

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

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

Representations

A tritruncated 6-simplex has the following Coxeter diagrams:

• o3o3x3x3o3o () (full symmetry)
• ooo3xoo3xux3oox3ooo&#xt (A₅ axial, facet-first)

Gallery

• 

  A₅ orthographic projection

• 

  A₄

• 

  A₃

• 

  A₂

External links

• Klitzing, Richard. "fe".
• Wikipedia contributors. "Tritruncated 6-simplex".