Great bicantitruncatotetracontoctachoron

Great bicantitruncatotetracontoctachoron
Rank	4
Type	Isogonal
Notation
Bowers style acronym	Gobcotic
Coxeter diagram	ao3bc4cb3oa&#zd (c > b+(2+√2)a)
Elements
Cells	288 tetragonal disphenoids, 576 wedges, 144 ditetragonal trapezoprisms, 48 great rhombicuboctahedra
Faces	1152 isosceles triangles, 1152 isosceles trapezoids, 576 rectangles, 192 ditrigons, 288 ditetragons
Edges	576+576+1152+1152
Vertices	1152
Vertex figure	Bi-apiculated tetrahedron
Measures (edge length 1)
Central density	1
Related polytopes
Army	Gobcotic
Regiment	Gobcotic
Dual	Great bimetatetracontoctachoron
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	F4×2, order 2304
Convex	Yes
Nature	Tame

The great bicantitruncatotetracontoctachoron or gobcotic is a convex isogonal polychoron that consists of 48 great rhombicuboctahedra, 144 ditetragonal trapezoprisms, 576 wedges, and 288 tetragonal disphenoids. 2 great rhombicuboctahedra, 2 ditetragonal trapezoprisms, 3 wedges, and 1 tetragonal disphenoid 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 great rhombated icositetrachora. In this case, if the great rhombated icositetrachora are of the form a3b4c3o, then c must be greater than $b+(2+{\sqrt {2}})a$ (producing the truncated tetracontoctachoron in the limiting case). The lacing edges generally have length ${\sqrt {(2-{\sqrt {2}})a^{2}+(6-4{\sqrt {2}})a(b-c)+(6-4{\sqrt {2}})(b-c)^{2}}}$.