Transitional bicantitruncatotetracontoctachoron
| Transitional bicantitruncatotetracontoctachoron | |
|---|---|
| Rank | 4 |
| Type | Isogonal |
| Notation | |
| Bowers style acronym | Tabcatic |
| Coxeter diagram | ao3bc4cb3oa&#zd (c = b+1/2) |
| Elements | |
| Cells | 192 triangular trapezorhombihedra, 144 ditetragonal trapezoprisms, 48 truncated cubes |
| Faces | 384 triangles 1152 isosceles trapezoids, 288 squares, 288 ditetragons |
| Edges | 576+1152+1152 |
| Vertices | 1152 |
| Vertex figure | Isosceles trapezoidal pyramid |
| Measures (edge length 1) | |
| Central density | 1 |
| Related polytopes | |
| Army | Tabcatic |
| Regiment | Tabcatic |
| Dual | Transitional bimetatetracontoctachoron |
| Abstract & topological properties | |
| Euler characteristic | 0 |
| Orientable | Yes |
| Properties | |
| Symmetry | F4×2, order 2304 |
| Convex | Yes |
| Nature | Tame |
The transitional bi-canti-truncato-decachoron or tabcatic is a convex isogonal polychoron that consists of 48 truncated cubes, 144 ditetragonal trapezoprisms, and 192 triangular trapezorhombihedra. 1 truncated cube, 2 ditetrgonal trapezoprisms, and 2 triangular trapezorhombihedra join at each verex.
It can also be formed as the convex hull of 2 oppositely oriented semi-uniform variants of the great rhombated icositetrachoron, where if the great rhombated icositetrachora are of the form a3b4c3o, then c = b+a/2. It is one of five polychora (including two transitional cases) formed from two great rhombated icositetrachora, and is the transitional point between the small bicantitruncatotetracontoctachoron and medial bicantitruncatotetracontoctachoron.
Using the ratio method, the lowest possible ratio between the longest and shortest edges is .
