Disnub disicositetrachoron
| Disnub disicositetrachoron | |
|---|---|
| Rank | 4 |
| Type | Uniform |
| Space | Spherical |
| Notation | |
| Bowers style acronym | Disdi |
| Elements | |
| Cells | 24 small stellated dodecahedra, 24 great dodecahedra, 96 semicupolaically-faceted great icosahedra, 96 semicupolaically-faceted icosahedra |
| Faces | 96+576 triangles, 288 pentagons, 288 pentagrams |
| Edges | 96+144+576 |
| Vertices | 96 |
| Vertex figure | Faceted tridiminished dodecahedron |
| Measures (edge length 1) | |
| Circumradius | 1 |
| Hypervolume | Undefined |
| Related polytopes | |
| Army | Sadi |
| Regiment | Disdi |
| Conjugate | Disnub disicositetrachoron |
| Abstract & topological properties | |
| Orientable | No |
| Properties | |
| Convex | No |
| Nature | Feral |
The disnub disicositetrachoron, or disdi, is a nonconvex scaliform polychoron that consists of 24 small stellated dodecahedra, 24 great dodecahedra, 96 regular semicupolaically-faceted great icosahedra, and 96 semicupolaically-faceted icosahedra. 3 small stellated dodecahedra, 3 great dodecahedra, 9 semicupolaically-faceted great icosahedra, and 9 semicupolaically-faceted icosahedra meet at each vertex.
It can be thought as a kind of sub-symmetrical faceting of the small stellated hecatonicosachoron.
It was found in January 2006 by Mason Green, along with the medial snub disicositetrachoron. ~15 years later, several hundred uniform polychora would be found in its regiment, starting with the snub hexecontatetrasnub-snub disoctachoron by Polytope Discord user _Geometer.
Vertex coordinates[edit | edit source]
The vertices of a disnub disicositetrachoron of edge length 1, centered at the origin, are given by all even permutations of:
External links[edit | edit source]
- Bowers, Jonathan. "Category S3: Special Scaliforms" (#S32).
- Klitzing, Richard. "disdi".