Great birhombatotetracontoctachoron

Great birhombatotetracontoctachoron
Rank	4
Type	Isogonal
Notation
Bowers style acronym	Gabric
Coxeter diagram	ao3ob4bo3oa&#zc (b:a > 2+√2)
Elements
Cells	288 tetragonal disphenoids, 576 rectangular pyramids, 144 square antiprisms, 48 small rhombicuboctahedra
Faces	192 triangles, 1152+1152 isosceles triangles, 288 squares, 576 rectangles
Edges	576+1152+1152
Vertices	576
Vertex figure	Laterowedged wedge
Measures (edge length 1)
Central density	1
Related polytopes
Army	Gabric
Regiment	Gabric
Dual	Great biorthotetracontoctachoron
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	F4×2, order 2304
Convex	Yes
Nature	Tame

The great birhombatotetracontoctachoron or gabric is a convex isogonal polychoron that consists of 48 small rhombicuboctahedra, 144 square antiprisms, 576 rectangular pyramids and 288 tetragonal disphenoids. 2 small rhombicuboctahedra, 2 square antiprisms, 5 rectangular pyramids, and 2 tetragonal disphenoids join at each vertex.

It is one of a total of five distinct polychora (including two transitional cases) that can be obtained as the convex hull of two opposite small rhombated icositetrachora. In this case, the ratio between the edges of the small rhombated icositetrachoron a3o4b3o is greater than b:a = $2+{\sqrt {2}}$ (which produces the rectified tetracontoctachoron in the limiting case). The lacing edges generally have length ${\sqrt {(2-{\sqrt {2}})a^{2}-(6-4{\sqrt {2}})ab+(6-4{\sqrt {2}})b^{2}}}$.

External links

• Klitzing, Richard. "gabric".