Transitional biprismatorhombatotetracontoctachoron
Transitional biprismatorhombatotetracontoctachoron  

File:Transitional biprismatorhombatotetracontoctachoron.png  
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  F_{4}×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 semiuniform 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.

Orthoaligned great rhombicuboctahedron