Transitional biprismatorhombatotetracontoctachoron
Transitional biprismatorhombatotetracontoctachoron | |
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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 = . 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.
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Orthoaligned great rhombicuboctahedron