Tetrahedral transitional biomnisnub decachoron
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| Tetrahedral transitional biomnisnub decachoron | |
|---|---|
| File:Tetrahedral transitional biomnisnub decachoron.png | |
| Rank | 4 |
| Type | Isogonal |
| Notation | |
| Bowers style acronym | Tetbosid |
| Elements | |
| Cells | 120 irregular tetrahedra, 60 phyllic disphenoids, 30 rhombic disphenoids, 20 triangular gyroprisms, 10 gyrated great rhombitetratetrahedra |
| Faces | 120+120+120+120+120 scalene triangles, 40 triangles, 20 ditrigons |
| Edges | 60+60+60+60+60+120+120 |
| Vertices | 120 |
| Vertex figure | 9-vertex polyhedron with 1 pentagon, 2 tetragons, and 7 triangles |
| Measures (edge length 1) | |
| Central density | 1 |
| Related polytopes | |
| Army | Tetbosid |
| Regiment | Tetbosid |
| Dual | Transitional intersected enneahedral hecatonicosachoron |
| Abstract & topological properties | |
| Euler characteristic | 0 |
| Orientable | Yes |
| Properties | |
| Symmetry | (A4×2)+, order 120 |
| Convex | Yes |
| Nature | Tame |
The tetrahedral transitional biomnisnub decachoron or tetbosid is a convex isogonal polychoron that consists of 10 gyrated great rhombitetratetrahedra, 20 triangular antiprisms, 30 rhombic disphenoids, 60 phyllic disphenoids, and 120 irregular tetrahedra. 2 gyrated great rhombitetratetrahedra, 1 triangular gyroprism, 1 rhombic disphenoid, 2 phyllic disphenoids, and 4 irregular tetrahedra join at each vertex. It is one of a total of 8 polychora that can be obtained as the convex hull of 2 snub pentachora.
Using the ratio method, the lowest possible ratio between the longest and shortest edges is 1:a ≈ 1:1.91395, where a is the largest real root of 225a8-1500a6+3110a4-2556a2+849.
External links[edit | edit source]
- Bowers, Jonathan. "Pennic and Decaic Isogonals".