Great biomnisnub decachoron
| Great biomnisnub decachoron | |
|---|---|
| Rank | 4 |
| Type | Isogonal |
| Notation | |
| Bowers style acronym | Gabosid |
| Elements | |
| Cells | 120+120+120 irregular tetrahedra, 60+60 phyllic disphenoids, 30 rhombic disphenoids, 20+20 triangular gyroprisms, 10 snub tetrahedra |
| Faces | 120+120+120+120+120+120+120+120+120+120 scalene triangles, 40+40 triangles |
| Edges | 60+60+60+60+60+60+120+120+120+120 |
| Vertices | 120 |
| Vertex figure | 14-vertex polyhedron with 1 pentagon, 2 tetragons, and 17 triangles |
| Measures (edge length 1) | |
| Central density | 1 |
| Related polytopes | |
| Army | Gabosid |
| Regiment | Gabosid |
| Dual | Great tetradecahedral hecatonicosachoron |
| Abstract & topological properties | |
| Euler characteristic | 0 |
| Orientable | Yes |
| Properties | |
| Symmetry | (A4×2)+, order 120 |
| Convex | Yes |
| Nature | Tame |
The great biomnisnub decachoron or gabosid is a convex isogonal polychoron that consists of 10 snub tetrahedra, 40 triangular gyroprisms of two kinds, 30 rhombic disphenoids, 120 phyllic disphenoids of two kinds, and 360 irregular tetrahedra of three kinds. 1 snub tetrahedron, 2 triangular gyroprisms, 1 rhombic disphenoid, 4 phyllic disphenoids, and 12 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 opposite snub pentachora.
This polychoron resembles the medial biomnisnub decachoron in every way except for the vertex figure's topology, in which the medial version's 5-valence vertex is not adjacent to the 6- and 8-valence vertices, unlike the great biomnisnub decachoron.
External links[edit | edit source]
- Bowers, Jonathan. "Pennic and Decaic Isogonals".