Icositetrintercepted icositetrachoron
The icositetrintercepted icositetrachoron, or ini, is a nonconvex uniform polychoron that consists of 24 cuboctahedra and 24 truncated octahedra. 3 cuboctahedra and 6 truncated octahedra join at each vertex.
| Icositetrintercepted icositetrachoron | |
|---|---|
 | |
| Rank | 4 |
| Type | Uniform |
| Notation | |
| Bowers style acronym | Ini |
| Elements | |
| Cells | |
| Faces | 96 triangles, 144 squares, 96 hexagons |
| Edges | 288 |
| Vertices | 96 |
| Vertex figure | Triangular toroprism, edge lengths √2 (base edges), 1 (side edges of rectaangles), and √3 (side edges of triangles) |
| Edge figure | co 3 co 4 toe 6 toe 6 toe 4 |
| Measures (edge length 1) | |
| Circumradius | |
| Hypervolume | 68 |
| Dichoral angle | Co–3–co: 120° Co–4–toe: 90° Toe–6–toe: 60° |
| Central density | 6 |
| Number of external pieces | 168 |
| Level of complexity | 6 |
| Related polytopes | |
| Army | Rico |
| Regiment | Rico |
| Conjugate | None |
| Convex core | Icositetrachoron |
| Abstract & topological properties | |
| Flag count | 5760 |
| Euler characteristic | 96 |
| Orientable | Yes |
| Properties | |
| Symmetry | F4, order 1152 |
| Flag orbits | 5 |
| Convex | No |
| Nature | Wild |
It is wild because it has cuboctahedra intercepted by hexagons.
Cross-sections edit
Vertex coordinates edit
Its vertices are the same as those of its regiment colonel, the rectified icositetrachoron.
External links edit
- Bowers, Jonathan. "Category 3: Triangular Rectates" (#47).
- Bowers, Jonathan. "Category 6: Sphenoverts" (#47 - recount under tesseractic symmetry).
- Klitzing, Richard. "ini".