Medial biprismatorhombatotetracontoctachoron

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 $$a+\frac{2-\sqrt2}{2}b$$ (producing the transitional biprismatorhombatotetracontoctachoron) and a+2b (producing the truncated small prismatotetracontoctachoron). The lacing edges generally have length $$\sqrt{(6-4\sqrt2)b^2+(6-4\sqrt2)a(b-c)+(6-4\sqrt2)(b-c)^2+(2-\sqrt2)(a-c)^2}$$.