Snub hexecontatetrasnub-snub disoctachoron
The snub hexecontatetrasnub-snub disoctachoron, or siggissido, is a nonconvex uniform polychoron that consists of 8 icosahedra, 8 great icosahedra, 64+96 regular octahedra, and 192 tetrahedra. 1 icosahedron, 1 great icosahedron, 4+6 octahedra, and 8 tetrahedra join at each vertex.
| Snub hexecontatetrasnub-snub disoctachoron | |
|---|---|
 | |
| Rank | 4 |
| Type | Uniform |
| Notation | |
| Bowers style acronym | Siggissido |
| Elements | |
| Cells | 192 tetrahedra, 64+96 octahedra, 8 icosahedra, 8 great icosahedra |
| Faces | 64+64+96+96+96+192+192+192+192 triangles |
| Edges | 48+96+96+192+192+192 |
| Vertices | 96 |
| Vertex figure | Blend of pentagrammic cuploid and retropentagonal cuploid, edge length 1 |
| Measures (edge length 1) | |
| Circumradius | 1 |
| Hypervolume | Undefined |
| Related polytopes | |
| Army | Sadi |
| Regiment | Disdi |
| Conjugate | Snub hexecontatetrasnub-snub disoctachoron |
| Convex core | Tesseract |
| Abstract & topological properties | |
| Euler characteristic | –224 |
| Orientable | No |
| Properties | |
| Symmetry | B4/2, order 192 |
| Convex | No |
| Nature | Tame |
This polychoron has pyritotesseractic symmetry, with the icosahedra and great icosahedra acting as snub tetrahedra. It can be thought as a kind of sub-symmetrical faceting of the small stellated hecatonicosachoron. With all of its cells geometrically regular, it can be considered a semiregular polychoron.
It was discovered on January 28, 2021, by Polytope Discord user _Geometer. Following the discovery of six uniforms the previous year its discovery led to the find of several hundred additional uniforms in the same regiment.
Gallery edit
Vertex coordinates edit
The vertices of a snub hexecontatetrasnub-snub disoctachoron of edge length 1, centered at the origin, are given by all even permutations of:
External links edit
- Bowers, Jonathan. "Category 30: Idtessids" (#1856).