Great tetracontoctachoron

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Great tetracontoctachoron
Rank4
TypeUniform
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
Inradius
Hypervolume
Dichoral anglesQuith–3–quith: 120°
 Quith–8/3–quith: 45°
Central density73
Number of external pieces3840
Level of complexity60
Related polytopes
ArmyCont, edge length
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.

Gallery[edit | edit source]

Card with cell counts, vertex figure, and cross-sections.

Vertex coordinates[edit | edit source]

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

External links[edit | edit source]

  • Klitzing, Richard. "gic".