Faceted rectified icositetrachoron
The faceted rectified icositetrachoron, or frico, is a nonconvex uniform polychoron that consists of 24 cubes and 24 truncated octahedra. Two cubes and six truncated octahedra join at each vertex.
| Faceted rectified icositetrachoron | |
|---|---|
 | |
| Rank | 4 |
| Type | Uniform |
| Space | Spherical |
| Notation | |
| Bowers style acronym | Frico |
| Coxeter diagram | (     )/2 |
| Elements | |
| Cells | 24 cubes, 24 truncated octahedra |
| Faces | 144 squares, 96 hexagons |
| Edges | 288 |
| Vertices | 96 |
| Vertex figure | Triangular retroprism, edge lengths √2 (base) and √3 (sides) |
| Edge figure | cube 4 toe 6 toe 6 toe 4 |
| Measures (edge length 1) | |
| Circumradius | |
| Hypervolume | 39 |
| Dichoral angles | Toe–6–toe: 60° |
| Cube–4–toe: 45° | |
| Central density | 5 |
| Number of external pieces | 1032 |
| Level of complexity | 23 |
| Related polytopes | |
| Army | Rico |
| Regiment | Rico |
| Conjugate | None |
| Convex core | Icositetrachoron |
| Abstract & topological properties | |
| Euler characteristic | 0 |
| Orientable | Yes |
| Properties | |
| Symmetry | F4, order 1152 |
| Convex | No |
| Nature | Tame |
GalleryEdit
Vertex coordinatesEdit
Its vertices are the same as those of its regiment colonel, the rectified icositetrachoron.
External linksEdit
- Bowers, Jonathan. "Category 3: Triangular Rectates" (#46).
- Bowers, Jonathan. "Category 6: Sphenoverts" (#46 - recount under tesseractic symmetry).
- Klitzing, Richard. "frico".