Medial birhombatotetracontoctachoron

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Medial birhombatotetracontoctachoron
Rank4
TypeIsogonal
Notation
Bowers style acronymMabric
Coxeter diagramao3ob4bo3oa&#zc (b:a < 1/2)
Elements
Cells288 tetragonal disphenoids, 576 rectangular pyramids, 192 triangular prisms, 144 square antiprisms, 48 cuboctahedra
Faces384 triangles, 1152+1152 isosceles triangles, 288 squares, 576 rectangles,
Edges576+1152+1152
Vertices576
Vertex figureParatetrakis rectangular frustum
Measures (edge length 1)
Central density1
Related polytopes
ArmyMabric
RegimentMabric
DualMedial biorthotetracontoctachoron
Abstract & topological properties
Flag count46080
Euler characteristic0
OrientableYes
Properties
SymmetryF4×2, order 2304
ConvexYes
NatureTame

The medial birhombatotetracontoctachoron or mabric is a convex isogonal polychoron that consists of 48 cuboctahedra, 144 square antiprisms, 192 triangular prisms, 576 rectangular pyramids, and 288 tetragonal disphenoids 1 cuboctahedron, 2 square antiprisms, 2 triangular prisms, 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 icositetrachora. In this case, the4 ratio between the edges of the small rhombated pentachoron a3o4b3o is less than b:a = 1/2 (which produces the rectified small prismatotetracontoctachoron in the limiting case). The lacing edges generally have length .

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