Great biomnitruncatotetracontoctachoron

Great biomnitruncatotetracontoctachoron
Rank	4
Type	Isogonal
Notation
Bowers style acronym	Gabotic
Coxeter diagram	ad3bc4cb3da&#ze
Elements
Cells	288 rectangular trapezoprisms, 384 ditrigonal frustums, 192 ditrigonal prisms, 144 ditetragonal trapezoprisms, 48 great rhombicuboctahedra
Faces	1152+1152 isosceles trapezoids, 576+576 rectangles, 384+384 ditrigons, 288 ditetragons
Edges	1152+1152+1152+1152+1152
Vertices	2304
Vertex figure	Irregular triangular tegum
Measures (edge length 1)
Central density	1
Related polytopes
Army	Gabotic
Regiment	Gabotic
Dual	Great biomnistellatotetracontoctachoron
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	F4×2, order 2304
Convex	Yes
Nature	Tame

The great biomnitruncatotetracontoctachoron or gabotic is a convex isogonal polychoron that consists of 48 great rhombicuboctahedra, 144 ditetragonal trapezoprisms, 192 ditrigonal prisms, 384 ditrigonal frustums, and 288 rectangular trapezoprisms. 2 ditrigonal frustums and 1 of each of the other 4 cell types join at each vertex.

It is one of a total of four distinct polychora (including two transitional cases) that can be obtained as the convex hull of two opposite great disprismatoicositetricositetrachora (that is, variants of the great prismatotetracontoctachoron with single F4 symmetry). If the great disprismatoicositetricositetrachora are of the form a3b4c3d, then the lacing edges generally have length ${\sqrt {(2-{\sqrt {2}})(a-d)^{2}+(6-4{\sqrt {2}})(b-c)^{2}+(6-4{\sqrt {2}})(a-d)(b-c)}}$.

This polychoron can be alternated into a great omnisnub bitetracontoctachoron, which is also nonuniform.