Great bitetracontoctachoron

Great bitetracontoctachoron
Rank4
TypeNoble
SpaceSpherical
Notation
Bowers style acronymGibic
Coxeter diagramo3m4/3m3o
Elements
Cells288 tetragonal disphenoids
Faces576 isosceles triangles
Edges144+192
Vertices48
Vertex figureGreat triakis octahedron
Measures (based on two icositetrachora of edge length 1)
Dichoral angle${\displaystyle \arccos\left(\frac{2\sqrt2-1}4\right) ≈ 62.79943°}$
Related polytopes
ArmyBicont
RegimentGibic
DualGreat tetracontoctachoron
ConjugateBitetracontoctachoron
Abstract & topological properties
OrientableYes
Properties
SymmetryF4×2, order 2304
ConvexNo
NatureTame

The great bitetracontoctachoron or gibic is a nonconvex noble polychoron with 288 tetragonal disphenoids as cells. 24 cells join at each vertex, with the vertex figure being a great triakis octahedron.

The ratio between the longest and shortest edges is 1:${\displaystyle \sqrt{2+\sqrt2}}$ ≈ 1:1.84776.

Vertex coordinates

Coordinates for the vertices of a great bitetracontoctachoron of circumradius 1, centered at the origin, are the same as those of a bitetracontoctachoron of the same circumradius. They are given by all permutations of:

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