Medial bicantitruncatodecachoron

Medial bicantitruncatodecachoron
Rank	4
Type	Isogonal
Notation
Bowers style acronym	Mobcated
Coxeter diagram	ao3bc3cb3oa&#zd (b+a/2 < c < b+3a)
Elements
Cells	30 tetragonal disphenoids, 40 triangular cupolas, 20 ditrigonal trapezoprisms, 10 truncated tetrahedra
Faces	40 triangles, 120 isosceles triangles, 120 isosceles trapezoids, 20+40 ditrigons
Edges	60+60+120+120
Vertices	120
Vertex figure	Monoaugmented isosceles trapezoidal pyramid
Measures (edge length 1)
Central density	1
Related polytopes
Army	Mobcated
Regiment	Mobcated
Dual	Medial bimetadecachoron
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	A4×2, order 240
Convex	Yes
Nature	Tame

The medial bicantitruncatodecachoron or mobcated is a convex isogonal polychoron that consists of 10 truncated tetrahedra, 20 ditrigonal trapezoprisms, 40 triangular cupolas, and 30 tetragonal disphenoids. 1 truncated tetrahedron, 2 ditrigonal 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 pentachora. In this case, if the great rhombated pentachora are of the form a3b3c3o, then c must be between b+a/2 (producing the transitional bicantitruncatodecachoron) and b+3a (producing the truncated decachoron). The lacing edges generally have length ${\sqrt {\frac {3a^{2}+2b^{2}+2c^{2}+2ab-2ac-4bc}{5}}}$.

External links

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