Medial birhombatodecachoron

Medial birhombatodecachoron
Rank	4
Type	Isogonal
Notation
Bowers style acronym	Mabred
Coxeter diagram	ao3ob3bo3oa&#zc (b:a < 1/2)
Elements
Cells	30 tetragonal disphenoids, 60 rectangular pyramids, 10 octahedra, 20 triangular antiprisms, 20 triangular prisms
Faces	40+40 triangles, 120+120 isosceles triangles, 60 rectangles
Edges	60+120+120
Vertices	60
Vertex figure	Paratetrakis rectangular frustum
Measures (edge length 1)
Central density	1
Related polytopes
Army	Mabred
Regiment	Mabred
Dual	Medial biorthodecachoron
Abstract & topological properties
Flag count	4800
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	A4×2, order 240
Convex	Yes
Nature	Tame

The medial birhombatodecachoron or mabred is a convex isogonal polychoron that consists of 10 octahedra, 20 triangular prisms, 20 triangular antiprisms, 60 rectangular pyramids, and 30 tetragonal disphenoids. 1 octahedron, 2 triangular prisms, 2 triangular antiprisms, 5 rectangular pyramids, and 2 tetragonal disphenoids 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 small rhombated pentachora. In this case, the ratio between the edges of the small rhombated pentachoron a3o3b3o is less than b:a = 1/2 (which produces the rectified small prismatodecachoron in the limiting case). The lacing edges generally have length ${\sqrt {\frac {3a^{2}-2ab+2b^{2}}{5}}}$.

External links

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

• Klitzing, Richard. "mabred".