Great tetracontoctachoron

Great tetracontoctachoron
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Gic
Coxeter diagram	o3x4/3x3o ()
Elements
Cells	48 quasitruncated hexahedra
Faces	192 triangles, 144 octagrams
Edges	576
Vertices	288
Vertex figure	Tetragonal disphenoid, edge lengths 1 (base) and √2–√2 (sides)
Edge figure	quith 8/3 quith 8/3 quith 3
Measures (edge length 1)
Circumradius	$2-\sqrt2 ≈ 0.58579$
Inradius	$\frac{3-2\sqrt2}{2} ≈ 0.085786$
Hypervolume	$14\left(17-12\sqrt2\right) ≈ 0.41212$
Dichoral angles	Quith–3–quith: 120°
	Quith–8/3–quith: 45°
Central density	73
Number of external pieces	3840
Level of complexity	60
Related polytopes
Army	Cont, edge length $3-2\sqrt2$
Regiment	Gic
Dual	Great bitetracontoctachoron
Conjugate	Tetracontoctachoron
Convex core	Tetracontoctachoron
Abstract & topological properties
Flag count	6912
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	F4×2, order 2304
Convex	No
Nature	Tame

The great tetracontoctachoron, or gic, is a nonconvex noble uniform polychoron that consists of 48 quasitruncated hexahedra as cells. Four cells join at each vertex. It can be considered to be the biquasitruncation of the icositetrachoron and is conjugate to the convex tetracontoctachoron.

The vertex-angle is 1/288.

Gallery

Vertex coordinates

Coordinates for the vertices of a great tetracontoctachoron of edge length 1 are all permutations of:

• $\left(±(\sqrt2-1),\,±\frac{2-\sqrt2}{2},\,±\frac{2-\sqrt2}{2},\,0\right),$
• $\left(±\frac{3-2\sqrt2}{2},\,±\frac{\sqrt2-1}{2},\,±\frac{\sqrt2-1}{2},\,±\frac12\right).$

External links

• Bowers, Jonathan. "Category 7: Bitruncates" (#305).

• Klitzing, Richard. "gic".