Transitional biprismatorhombatotetracontoctachoron

The transitional biprismatorhombatotetracontoctachoron or tabiparc is a convex isogonal polychoron that consists of 48 orthoaligned great rhombicuboctahedra, 288 rectangular trapezoprisms, and 192 triangular prisms. 2 orthoaligned great rhombicuboctahedra, 2 rectangular trapezoprisms, and 1 triangular prism join at each vertex.

Transitional biprismatorhombatotetracontoctachoron
File:Transitional biprismatorhombatotetracontoctachoron.png
Rank4
TypeIsogonal
Notation
Bowers style acronymTabiparc
Coxeter diagramac3bo4ob3ca&#zd (c = a+(2-2)b/2)
Elements
Cells192 triangular prisms, 288 rectangular trapezoprisms, 48 orthoaligned great rhombicuboctahedra
Faces384 triangles, 576 rectangles, 1152 isosceles trapezoids, 144 ditetragons
Edges576+1152+1152
Vertices1152
Vertex figureIsosceles trapezoidal pyramid
Measures (edge length 1)
Central density1
Related polytopes
ArmyTabiparc
RegimentTabiparc
DualTransitional bicrystallorthotetracontoctachoron
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryF4×2, order 2304
ConvexYes
NatureTame

It can also be formed as the convex hull of 2 oppositely oriented semi-uniform variants of the prismatorhombated icositetrachoron, where if the prismatorhombated icositetrachora are of the form a3b4o3c, then c = . It is one of five polychora (including two transitional cases) formed from two prismatorhombated icositetrachora, and is the transitional point between the small biprismatorhombatotetracontoctachoron and medial biprismatorhombatotetracontoctachoron.

Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1: ≈ 1:1.54120.