Truncated 6-orthoplex

Truncated 6-orthoplex
(OFF file)
Rank	6
Type	Uniform
Notation
Bowers style acronym	Tag
Coxeter diagram	o4o3o3o3x3x ()
Elements
Peta	12 5-orthoplexes, 64 truncated 5-simplices
Tera	384 pentachora, 192 truncated pentachora
Cells	960 tetrahedra, 240 truncated tetrahedra
Faces	960 triangles, 160 hexagons
Edges	60+480
Vertices	120
Vertex figure	Hexadecachoric pyramid, edge lengths 1 (base) and √3 (sides)
Measures (edge length 1)
Circumradius	${\frac {\sqrt {10}}{2}}\approx 1.58114$
Hypervolume	${\frac {241}{30}}\approx 8.03333$
Dipetal angles	Tix–tip–tix: $\arccos \left(-{\frac {2}{3}}\right)\approx 131.81032^{\circ }$
	Tac–pen–tix: $\arccos \left(-{\frac {\sqrt {6}}{6}}\right)\approx 114.09484^{\circ }$
Central density	1
Number of external pieces	76
Level of complexity	6
Related polytopes
Army	Tag
Regiment	Tag
Conjugate	None
Abstract & topological properties
Flag count	276480
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	B6, order 46080
Convex	Yes
Nature	Tame

The truncated 6-orthoplex, also called the truncated hexacontatetrapeton or tag, is a convex uniform 6-polytope. It consists of 64 truncated 5-simplices and 12 5-orthoplexes. 16 truncated 5-simplices and 1 5-orthoplex join at each vertex. As the name suggests, it is the truncation of the 6-orthoplex.

Vertex coordinates

The vertices of a truncated 6-orthoplex of edge length 1 are given by all permutations of:

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

Representations

A truncated 6-orthoplex has the following Coxeter diagrams:

• o4o3o3o3x3x () (full symmetry)
• o3o3o3x3x *b3o () (D₆ symmetry)

Gallery

• 

  B₅ orthographic projection

• 

  B₄

• 

  B₃

• 

  B₂

• 

  A₅

• 

  A₃

Related polytopes

The truncated 6-orthoplex is the colonel of a two-member regiment that also includes the truncated triacontadihemihexeract. The regiment also include 2 scaliforms with doubled icosahedral step prism symmetry.

External links

• Klitzing, Richard. "tag".
• Wikipedia contributors. "Truncated 6-orthoplex".