Medial bicantitruncatotetracontoctachoron

Medial bicantitruncatotetracontoctachoron
Rank	4
Type	Isogonal
Notation
Bowers style acronym	Mobcotic
Coxeter diagram	ao3bc4cb3oa&#zd (b+a/2 < c < b+(2+√2)a)
Elements
Cells	288 tetragonal disphenoids, 384 triangular cupolas, 144 ditetragonal trapezoprisms, 48 truncated cubes
Faces	384 triangles, 1152 isosceles triangles, 1152 isosceles trapezoids, 288 ditetragons, 192 ditrigons
Edges	576+576+1152+1152
Vertices	1152
Vertex figure	Monoaugmented isosceles trapezoidal pyramid
Measures (edge length 1)
Central density	1
Related polytopes
Army	Mobcotic
Regiment	Mobcotic
Dual	Medial bimetatetracontoctachoron
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	F4×2, order 2304
Convex	Yes
Nature	Tame

The medial bicantitruncatotetracontoctachoron or mobcotic is a convex isogonal polychoron that consists of 48 truncated cubes, 144 ditetragonal trapezoprisms, 384 triangular cupolas, and 288 tetragonal disphenoids. 1 tuncated cube, 2 ditetragonal trapezoprisms, 3 triangular cupolas, 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 between $b+a/2$ (producing the transitional bicantitruncatotetracontoctachoron) and $b+(2+{\sqrt {2}})a$ (producing the truncated tetracontoctachoron). The lacing edges generally have length ${\sqrt {(2-{\sqrt {2}})a^{2}+(6-4{\sqrt {2}})a(b-c)+(6-4{\sqrt {2}})(b-c)^{2}}}$.