Great bitetracontoctachoron

Great bitetracontoctachoron
(OFF file)
Rank	4
Type	Noble
Notation
Bowers style acronym	Gibic
Coxeter diagram	o3m4/3m3o ()
Elements
Cells	288 tetragonal disphenoids
Faces	576 isosceles triangles
Edges	144+192
Vertices	48
Vertex figure	Great triakis octahedron
Measures (based on two icositetrachora of edge length 1)
Dichoral angle	$\arccos \left({\frac {2{\sqrt {2}}-1}{4}}\right)\approx 62.79943^{\circ }$
Related polytopes
Army	Bicont
Regiment	Gibic
Dual	Great tetracontoctachoron
Conjugate	Bitetracontoctachoron
Abstract & topological properties
Flag count	6912
Orientable	Yes
Properties
Symmetry	F4×2, order 2304
Flag orbits	3
Convex	No
Nature	Tame

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:${\sqrt {2+{\sqrt {2}}}}$ ≈ 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:

• $\left(\pm 1,\,0,\,0,\,0\right)$,
• $\left(\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {1}{2}}\right)$,
• $\left(\pm {\frac {\sqrt {2}}{2}},\,\pm {\frac {\sqrt {2}}{2}},\,0,\,0\right)$.