Medial biprismatorhombatotetracontoctachoron

Medial biprismatorhombatotetracontoctachoron
Rank	4
Type	Isogonal
Notation
Bowers style acronym	Mabiparc
Coxeter diagram	ac3bo4ob3ca&#zd (a+(2-√2)b/2 < c < a+2b)
Elements
Cells	192 triangular prisms, 288 rectangular trapezoprisms, 144 square antiprisms, 384 triangular cupolas, 48 truncated octahedra
Faces	384 triangles, 1152 isosceles triangles, 288 squares, 576 rectangles, 1152 isosceles trapezoids, 384 ditrigons
Edges	576+1152+1152+1152
Vertices	1152
Vertex figure	7-vertex polyhedron with 2 trapezoids and 6 triangles
Measures
Central density	1
Related polytopes
Army	Mabiparc
Regiment	Mabiparc
Dual	Medial bicrystallorthotetracontoctachoron
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	F4×2, order 2304
Convex	Yes
Nature	Tame

The medial biprismatorhombatotetracontoctachoron or mabiparc is a convex isogonal polychoron that consists of 48 truncated octahedra, 144 square antiprisms, 288 rectangular trapezoprisms, 192 triangular prisms, and 384 triangular cupolas. 1 truncated octahedron, 1 square antiprism, 2 rectangular trapezoprisms, 1 triangular prism, and 3 triangular cupolas join 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 prismatorhombated icositetrachora. In this case, if the prismatorhombated icositetrachora are of the form a3b4o3c, then c must be between $a+{\frac {2-{\sqrt {2}}}{2}}b$ (producing the transitional biprismatorhombatotetracontoctachoron) and a+2b (producing the truncated small prismatotetracontoctachoron). The lacing edges generally have length ${\sqrt {(6-4{\sqrt {2}})b^{2}+(6-4{\sqrt {2}})a(b-c)+(6-4{\sqrt {2}})(b-c)^{2}+(2-{\sqrt {2}})(a-c)^{2}}}$.