# Great tetracontoctachoron

Great tetracontoctachoron Rank4
TypeUniform
SpaceSpherical
Notation
Bowers style acronymGic
Coxeter diagramo3x4/3x3o (         )
Elements
Cells48 quasitruncated hexahedra
Faces192 triangles, 144 octagrams
Edges576
Vertices288
Vertex figureTetragonal disphenoid, edge lengths 1 (base) and 2–2 (sides)
Edge figurequith 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 anglesQuith–3–quith: 120°
Quith–8/3–quith: 45°
Central density73
Number of external pieces3840
Level of complexity60
Related polytopes
ArmyCont, edge length $3-2\sqrt2$ RegimentGic
DualGreat bitetracontoctachoron
ConjugateTetracontoctachoron
Convex coreTetracontoctachoron
Abstract & topological properties
Flag count6912
Euler characteristic0
OrientableYes
Properties
SymmetryF4×2, order 2304
ConvexNo
NatureTame

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.

## Vertex coordinates

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

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