Transitional biprismatorhombatotetracontoctachoron

Transitional biprismatorhombatotetracontoctachoron
Rank	4
Type	Isogonal
Notation
Bowers style acronym	Tabiparc
Coxeter diagram	ac3bo4ob3ca&#zd (c = a+(2-√2)b/2)
Elements
Cells	192 triangular prisms, 288 rectangular trapezoprisms, 48 orthoaligned great rhombicuboctahedra
Faces	384 triangles, 576 rectangles, 1152 isosceles trapezoids, 144 ditetragons
Edges	576+1152+1152
Vertices	1152
Vertex figure	Isosceles trapezoidal pyramid
Measures (edge length 1)
Central density	1
Related polytopes
Army	Tabiparc
Regiment	Tabiparc
Dual	Transitional bicrystallorthotetracontoctachoron
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	F4×2, order 2304
Convex	Yes
Nature	Tame

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.

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 = $a+{\frac {2-{\sqrt {2}}}{2}}b$. 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:${\frac {2+{\sqrt {4-2{\sqrt {2}}}}}{2}}$ ≈ 1:1.54120.

• 

  Orthoaligned great rhombicuboctahedron