Tritruncated 6-cube

Tritruncated 6-cube
(OFF file)
Rank	6
Type	Uniform
Notation
Bowers style acronym	Xog
Coxeter diagram	o4o3x3x3o3o ()
Elements
Peta	64 bitruncated 5-simplices, 12 bitruncated 5-orthoplexes
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	${\frac {\sqrt {26}}{2}}\approx 2.54951$
Hypervolume	${\frac {17407}{45}}\approx 386.82222$
Dipetal angles	Bittix–tip–bittix: $\arccos \left(-{\frac {2}{3}}\right)\approx 131.81032^{\circ }$
	Bittint–deca–bittix: $\arccos \left(-{\frac {\sqrt {6}}{6}}\right)\approx 114.09484^{\circ }$
	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
Flag count	921600
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	B6, order 46080
Convex	Yes
Nature	Tame

The tritruncated 6-cube, also called the tritruncated 6-orthoplex, tritruncated hexeract, tritruncated hexacontatetrapeton, hexeractihexacontatetrapeton, or xog, is a convex uniform 6-polytope. It consists of 12 bitruncated 5-orthoplexes and 64 bitruncated 5-simplices. 3 bitruncated 5-orthoplexes and 4 bitruncated 5-simplices join at each vertex. As the name suggests, it is the tritruncation of either the 6-cube or its dual 6-orthoplex.

Vertex coordinates

The vertices of a tritruncated 6-cube of edge length 1 are given by all permutations of:

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

Representations

A tritruncated 6-cube has the following Coxeter diagrams:

• o4o3x3x3o3o () (full symmetry)
• o3x3x3o3o *b3o () (D₆ symmetry)

Gallery

• 

  B₅ orthographic projection

• 

  B₄

• 

  B₃

• 

  B₂

• 

  A₅

• 

  A₃

Related polytopes

The tritruncated 6-cube is the colonel of a two-member regiment that also includes the tritruncated triacontadihemihexeract.

External links

• Klitzing, Richard. "xog".
• Wikipedia contributors. "Tritruncated 6-cube".