Tesseractihemioctachoron
| Tesseractihemioctachoron | |
|---|---|
 | |
| Rank | 4 |
| Type | Uniform |
| Notation | |
| Bowers style acronym | Tho |
| Coxeter diagram | (x3o3o3o3/2*1)/2 (    /2) |
| Elements | |
| Cells | 8 tetrahedra, 4 octahedra |
| Faces | 32 triangles |
| Edges | 24 |
| Vertices | 8 |
| Vertex figure | Tetrahemihexahedron, edge length 1 |
| Edge figure | tet 3 oct 3 tet 3 oct 3 |
| Measures (edge length 1) | |
| Circumradius | |
| Dichoral angle | 60° |
| Number of external pieces | 40 |
| Level of complexity | 5 |
| Related polytopes | |
| Army | Hex |
| Regiment | Hex |
| Company | Hex |
| Dual | Tesseractihemioctacron |
| Conjugate | None |
| Abstract & topological properties | |
| b0 | 1 |
| b1 | 0 |
| b2 | 3 |
| b3 | 0 |
| Flag count | 384 |
| Euler characteristic | 4 |
| Orientable | No |
| Properties | |
| Symmetry | D4, order 192 |
| Flag orbits | 2 |
| Convex | No |
| Nature | Tame |
The tesseractihemioctachoron, or tho, is a uniform hemipolychoron. It has 8 regular tetrahedra and 4 central octahedra as cells, with 4 tetrahedra and 3 octahedra at each vertex in the form of a tetrahemihexahedron. It is the 4D demicross.
It is a faceting of the hexadecachoron, analogous to how the tetrahemihexahedron is a faceting of the octahedron. It shares the hexadecachoron's vertices, edges, and faces. The 8 tetrahedra are half of those of the hexadecachoron, while the octahedra are its original vertex figures.
Notably, as well as being isogonal, the tesseractihemioctachoron is also edge- and face-transitive. It is one of only four non-regular uniform polychora to be vertex, edge, and face transitive.
Cross-sections[edit | edit source]
Vertex coordinates[edit | edit source]
Its vertices are the same as those of its regiment colonel, the hexadecachoron.
External links[edit | edit source]
- Bowers, Jonathan. "Category 1: Regular Polychora" (#17).
- Klitzing, Richard. "tho".