Trirectified 8-orthoplex

Trirectified 8-orthoplex
Rank	8
Type	Uniform
Notation
Bowers style acronym	Tark
Coxeter diagram	o4o3o3o3x3o3o3o ()
Elements
Zetta	256 trirectified 7-simplices 16 birectified 7-orthoplexes
Exa	1024+2048 birectified 6-simplices 112 rectified 6-orthoplexes
Peta	448 5-orthoplexes 1792+7168 rectified 5-simplices 7168 birectified 5-simplices
Tera	1792+14336 pentachora 10752+21504 rectified pentachora
Cells	8960+35840 tetrahedra 26880 octahedra
Faces	17920+35840 triangles
Edges	17920
Vertices	1120
Vertex figure	Tetrahedral-hexadecachoric duoprism, edge length 1
Measures (edge length 1)
Circumradius	${\sqrt {2}}\approx 1.41421$
Hypervolume	8
Dizettal angles	He–bril–he: $\arccos \left(-{\frac {3}{4}}\right)\approx 138.59038^{\circ }$
	Barz–bril–he: $\arccos \left(-{\frac {\sqrt {2}}{4}}\right)\approx 110.70481^{\circ }$
	Barz–rag–barz: 90°
Central density	1
Number of external pieces	272
Level of complexity	35
Related polytopes
Army	Tark
Regiment	Tark
Conjugate	None
Abstract & topological properties
Flag count	361267200
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	B8, order 10321920
Flag orbits	35
Convex	Yes
Nature	Tame

The trirectified 8-orthoplex, also called the trirectified diacosipentacontahexazetton, is a convex uniform 8-polytope. It consists of 16 birectified 7-orthoplexes and 256 trirectified 7-simplices. 4 birectified 7-orthoplexes and 16 trirectified 7-simplices join at each tetrahedral-hexadecachoric duoprismatic vertex. As the name suggests, it is the trirectification of the 8-orthoplex.

The trirectified 8-orthoplex can be vertex-inscribed into the 2₄₁ polytope.

Vertex coordinates

The vertices of a trirectified 8-orthoplex of edge length 1 are given by all permutations of:

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

Representations

A trirectified 8-orthoplex has the following Coxeter diagrams:

• o4o3o3o3x3o3o3o () (full symmetry)
• o3o3o3x3o3o3o *b3o () (D₈ symmetry)
• ooo4ooo3ooo3oxo3xox3ooo3ooo&#xt (B₇ axial, birectified 7-orthoplex-first)

External links

• Klitzing, Richard. "tark".
• Wikipedia contributors. "Trirectified 8-orthoplex".