Hexeractihexacontatetrapeton

Hexeractihexacontatetrapeton
(OFF file)
Rank	6
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Xog
Coxeter diagram	o4o3x3x3o3o
Elements
Peta	64 bitruncated hexatera, 12 bitruncated triacontaditera
Tera	192 truncated pentachora, 384 decachora, 60 truncated hexadecachora
Cells	240 tetrahedra, 160 octahedra, 960+960 truncated tetrahedra
Faces	960+1280 triangles, 1920 hexagons
Edges	1440+1920
Vertices	960
Vertex figure	Square tettene, edge lengths 1 (base square and top triangle) and √3 (sides)
Measures (edge length 1)
Circumradius	$\frac{\sqrt{26}}{2} ≈ 2.54951$
Hypervolume	$\frac{17407}{45} ≈ 386.82222$
Dipetal angles	Bittix–tip–bittix: $\arccos\left(-\frac23\right) ≈ 131.81032°$
	Bittint–deca–bittix: $\arccos\left(-\frac{\sqrt6}{6}\right) ≈ 114.09484°$
	Bittit–thex–bittit: 90°
Central density	1
Number of external pieces	76
Level of complexity	20
Related polytopes
Army	Xog
Regiment	Xog
Conjugate	None
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	B6, order 46080
Convex	Yes
Nature	Tame

The hexeractihexacontatetrapeton, tritruncated hexeract, tritruncated hexacontatetrapeton, or xog, also called the tritruncated 6-cube or tritruncated 6-orthoplex, is a convex uniform polypeton. It consists of 12 bitruncated triacontaditera and 64 bitruncated hexatera. 3 bitruncated triacontaditera and 4 bitruncated hexatera join at each vertex. As the name suggests, it is the tritruncation of either the hexeract or its dual hexacontatetrapeton.

Vertex coordinates

The vertices of a hexeractihexacontatetrapeton of edge length 1 are given by all permutations of:

• $\left(±\sqrt2,\,±\sqrt2,\,±\sqrt2,\,±\frac{\sqrt2}{2},\,0,\,0\right).$

Representations

A hexeractihexacontatetrapeton has the following Coxeter diagrams:

• o4o3x3x3o3o (full symmetry)
• o3x3o *b3x3o3o () (D₆ symmetry)

Gallery

• 

  B₅ orthographic projection

• 

  B₄

• 

  B₃

• 

  B₂

• 

  A₅

• 

  A₃

External links

• Klitzing, Richard. "xog".

• Wikipedia Contributors. "Tritruncated 6-cube".