Truncated grand hexacosichoron

Truncated grand hexacosichoron
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Taggix
Coxeter diagram	o5/2o3x3x ()
Elements
Cells	600 truncated tetrahedra, 120 great icosahedra
Faces	2400 triangles, 1200 hexagons
Edges	720+3600
Vertices	1440
Vertex figure	Pentagrammic pyramid, edge lengths 1 (base) and √3 (sides)
Measures (edge length 1)
Circumradius	$\sqrt{\frac{23-9\sqrt5}{2}} \approx 1.19904$
Hypervolume	$25\frac{80\sqrt5-161}{4} \approx 111.78399$
Dichoral angles	Gike–3–tut: $\arccos\left(-\frac{\sqrt{7-3\sqrt5}}{4}\right) \approx 97.76124^\circ$
	Tut–6–tut: $\arccos\left(\frac{3\sqrt5-1}{8}\right) \approx 44.47751^\circ$
Central density	191
Number of external pieces	80760
Level of complexity	269
Related polytopes
Army	Semi-uniform Tex
Regiment	Tigfix
Conjugate	Truncated hexacosichoron
Convex core	Hexacosichoron
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	H4, order 14400
Convex	No
Nature	Tame

The truncated grand hexacosichoron, or taggix, is a nonconvex uniform polychoron that consists of 120 great icosahedra and 600 truncated tetrahedra. 1 great icosahedron and five truncated tetrahedra join at each vertex. As the name suggests, it can be obtained by truncating the grand hexacosichoron.

Cross-sections

Vertex coordinates

Its vertices are the same as those of its regiment colonel, the truncated great faceted hexacosichoron.

External links

• Bowers, Jonathan. "Category 2: Truncates" (#29).

• Klitzing, Richard. "taggix".