Rectified faceted hexacosichoron
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| Rectified faceted hexacosichoron | |
|---|---|
 | |
| Rank | 4 |
| Type | Uniform |
| Notation | |
| Bowers style acronym | Rofix |
| Coxeter diagram | o5/2o5x3o (     ) |
| Elements | |
| Cells | |
| Faces | |
| Edges | 3600 |
| Vertices | 720 |
| Vertex figure | Semi-uniform pentagrammic prism, edge lengths (1+√5)/2 (base) and 1 (side) |
| Edge figure | gad.id.id |
| Measures (edge length 1) | |
| Circumradius | |
| Hypervolume | |
| Dichoral angle | Gad–5–id: 144° Id–3–id: 120° |
| Central density | 4 |
| Number of external pieces | 2520 |
| Level of complexity | 11 |
| Related polytopes | |
| Army | Rox |
| Regiment | Rox |
| Conjugate | Rectified great faceted hexacosichoron |
| Convex core | Hecatonicosachoron |
| Abstract & topological properties | |
| Flag count | 43200 |
| Euler characteristic | –480 |
| Orientable | Yes |
| Properties | |
| Symmetry | H4, order 14400 |
| Flag orbits | 3 |
| Convex | No |
| Nature | Tame |
The rectified faceted hexacosichoron, or rofix, is a nonconvex uniform polychoron that consists of 120 great dodecahedra and 120 icosidodecahedra. Two great dodecahedra and five icosidodecahedra join at each pentagrammic prismatic vertex. As the name suggests, it can be obtained by rectifying the faceted hexacosichoron.
Cross-sections[edit | edit source]
Vertex coordinates[edit | edit source]
Its vertices are the same as those of its regiment colonel, the rectified hexacosichoron.
External links[edit | edit source]
- Bowers, Jonathan. "Category 5: Pentagonal Rectates" (#74).
- Klitzing, Richard. "rofix".
| truncations | ||||
|---|---|---|---|---|
| Name | OBSA | Schläfli symbol | CD diagram | Image |
| Small stellated hecatonicosachoron | sishi | {5/2,5,3} | |  |
| Rectified small stellated hecatonicosachoron | rasishi | r{5/2,5,3} | |  |
| Rectified faceted hexacosichoron | rofix | r{3,5,5/2} | | |
| Faceted hexacosichoron | fix | {3,5,5/2} | |  |
| (degenerate, quadruple cover of hi) | t{5/2,5,3} | | ||
| Small rhombated small stellated hecatonicosachoron | sirsashi | rr{5/2,5,3} | | |
| Prismatodishecatonicosachoron | padohi | t0,3{5/2,5,3} | | |
| Small hecatonicosihecatonicosachoron | shihi | 2t{5/2,5,3} | |  |
| Small rhombated faceted hexacosichoron | sirfix | rr{3,5,5/2} | |  |
| Truncated faceted hexacosichoron | tiffix | t{3,5,5/2} | |  |
| (degenerate, sirdhi + 720(10/2)) | t0,1,2{5/2,5,3} | | ||
| (degenerate, six fipady + 720 double covers of pip) | t0,1,3{5/2,5,3} | | ||
| Prismatorhombated stellated hecatonicosachoron | pirshi | t0,2,3{5/2,5,3} | | |
| Great rhombated faceted hexacosichoron | girfix | t1,2,3{5/2,5,3} | | |
| (degenerate, sripady + 720 double covers of pip) | t0,1,2,3{5/2,5,3} | | ||