Medial biprismatorhombatodecachoron

Medial biprismatorhombatodecachoron
Rank	4
Type	Isogonal
Notation
Bowers style acronym	Mabipard
Coxeter diagram	ac3bo3ob3ca&#zd (a+b/3 < c < a+2b)
Elements
Cells	20 triangular prisms, 20 triangular antiprisms, 30 rectangular trapezoprisms, 40 triangular cupolas, 10 truncated tetrahedra
Faces	40+40 triangles, 120 isosceles triangles, 60 rectangles, 120 isosceles trapezoids, 40 ditrigons
Edges	60+120+120+120
Vertices	120
Vertex figure	7-vertex polyhedron with with 6 triangles and 2 trapezoids
Measures (edge length 1)
Central density	1
Related polytopes
Army	Mabipard
Regiment	Mabipard
Dual	Medial bicrystallorthodecachoron
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	A4×2, order 240
Convex	Yes
Nature	Tame

The medial biprismatorhombatodecachoron or mabipard is a convex isogonal polychoron that consists of 10 truncated tetrahedra, 30 rectangular trapezoprisms, 20 triangular prisms, 20 triangular antiprisms, and 40 triangular cupolas. 1 truncated tetrahedron, 2 rectangular trapezoprisms, 1 triangular prism, 1 triangular antiprism, and 3 triangular cupolas 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 prismatorhombated pentachora. In this case, if the prismatorhombated pentachora are of the form a3b3o3c, then c must be between a+b/3 (producing the transitional biprismatorhombatodecachoron) and a+2b (producing the truncated small prismatodecachoron). The lacing edges generally have length ${\sqrt {\frac {3a^{2}+2b^{2}+3c^{2}+2ab-6ac-2bc}{5}}}$.

External links

• Bowers, Jonathan. "Pennic and Decaic Isogonals".