Small ditrigonary dishecatonicosachoron
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| Small ditrigonary dishecatonicosachoron | |
|---|---|
 | |
| Rank | 4 |
| Type | Uniform |
| Space | Spherical |
| Notation | |
| Bowers style acronym | Sidditdy |
| Coxeter diagram | (o3x5/2o3/2x5/3*a3*c *b5*d)/2 |
| Elements | |
| Cells | 120 small ditrigonary icosidodecahedra, 120 small ditrigonal dodecicosidodecahedra |
| Faces | 2400 triangles, 1440 pentagrams, 720 decagons |
| Edges | 7200 |
| Vertices | 1200 |
| Vertex figure | Crossed ditrigonal trapezoprism, edge lengths 1 and (√5–1)/2 (base) and √(5+√5)/2 (sides) |
| Measures (edge length 1) | |
| Circumradius | |
| Hypervolume | |
| Dichoral angles | Sidditdid–10–sidditdid: 144° |
| Sidtid–5/2–sidditdid: 72° | |
| Sidtid–3–sidditdid: 60° | |
| Related polytopes | |
| Army | Rahi |
| Regiment | Rissidtixhi |
| Conjugate | Great ditrigonary dishecatonicosachoron |
| Abstract & topological properties | |
| Euler characteristic | –1680 |
| Orientable | Yes |
| Properties | |
| Symmetry | H4, order 14400 |
| Convex | No |
| Nature | Tame |
The small ditrigonary dishecatonicosachoron, or sidditdy, is a nonconvex uniform polychoron that consists of 120 small ditrigonary icosidodecahedra and 120 small ditrigonal dodecicosidodecahedra. 2 small ditrigonary icosidodecahedra and 6 small ditrigonal dodecicosidodecahedra join at each vertex.
Vertex coordinates[edit | edit source]
Its vertices are the same as those of its regiment colonel, the rectified small ditrigonary hexacosihecatonicosachoron.
Related polychora[edit | edit source]
| Index | Name | OBSA | Company | Subcategory |
|---|---|---|---|---|
| 1147 | Rectified small ditrigonary hexacosihecatonicosachoron | Rissidtixhi | Rissidtixhi | Main nine |
| 1148 | Rectified ditrigonary dishecatonicosachoron | Ridtidohi | Ridtidohi | Main nine |
| 1149 | Rectified great ditrigonary hexacosihecatonicosachoron | Riggidtixhi | Riggidtixhi | Main nine |
| 1150 | Small ditrigonary dishecatonicosachoron | Sidditdy | Sidditdy | Main nine |
| 1151 | Retroditrigonary dishecatonicosachoron | Ridditdy | Ridditdy | Main nine |
| 1152 | Great ditrigonary dishecatonicosachoron | Gidditdy | Gidditdy | Main nine |
| 1153 | Ditrigonary hexacosidishecatonicosachoron | Dittixdy | Main nine | |
| 1154 | Ditrigonary trishecatonicosachoron | Dittathi | Main nine | |
| 1155 | Toroidal ditrigonary hexacosidishecatonicosachoron | Todtixady | Main nine | |
| 1156 | Small ditrigonary dishecatonicosihecatonicosachoron | Sidtid hihy | Sixteen trapezics | |
| 1157 | Ditrigonary hecatonicosidishecatonicosachoron | Dithidy | Sixteen trapezics |
External links[edit | edit source]
- Bowers, Jonathan. "Category 23: Rissidtixhi Regiment" (#1150).
- Klitzing, Richard. "sidditdy".