Great grand hecatonicosachoron
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| Great grand hecatonicosachoron | |
|---|---|
 | |
| Rank | 4 |
| Type | Regular |
| Notation | |
| Bowers style acronym | Gaghi |
| Coxeter diagram | x5o5/2o3o (     ) |
| Schläfli symbol | |
| Elements | |
| Cells | 120 great dodecahedra |
| Faces | 720 pentagons |
| Edges | 1200 |
| Vertices | 120 |
| Vertex figure | Great stellated dodecahedron, edge length (1+√5)/2 |
| Edge figure | gad 5 gad 5 gad 5 |
| Deep holes | Triangles |
| Measures (edge length 1) | |
| Circumradius | 1 |
| Edge radius | |
| Face radius | |
| Inradius | |
| Hypervolume | |
| Dichoral angle | 72° |
| Central density | 76 |
| Number of external pieces | 10800 |
| Level of complexity | 33 |
| Related polytopes | |
| Army | Ex, edge length |
| Regiment | Sishi |
| Dual | Great faceted hexacosichoron |
| Conjugate | Small stellated hecatonicosachoron |
| Convex core | Hecatonicosachoron |
| Abstract & topological properties | |
| Flag count | 14400 |
| Euler characteristic | –480 |
| Schläfli type | {5,5,3} |
| Orientable | Yes |
| Properties | |
| Symmetry | H4, order 14400 |
| Flag orbits | 1 |
| Convex | No |
| Nature | Tame |
The great grand hecatonicosachoron, or gaghi, also commonly called the great grand 120-cell, is one of the 10 regular Schläfli–Hess polychora. It has 120 great dodecahedra as cells, joining 3 to an edge and 12 to a vertex in the form of a great stellated dodecahedron.
It is a faceting of the small stellated hecatonicosachoron, sharing its vertices and edges. It is the only other regular polychoron to do so.
Cross-sections[edit | edit source]
Vertex coordinates[edit | edit source]
Its vertices are the same as those of its regiment colonel, the small stellated hecatonicosachoron.
Related polychora[edit | edit source]
Uniform polychoron compounds composed of great grand hecatonicosachora include:
- Great grand diacositetracontachoron (2)
- Great grand chirohexacosichoron (5)
- Great grand chirododecahedral hyperprismatochoron (6)
- Great grand dishexacosichoron (10)
- Great grand disdodecahedral hyperprismatochoron (12)
External links[edit | edit source]
- Bowers, Jonathan. "Category 1: Regular Polychora" (#11).
- Bowers, Jonathan. "How to Make Gaghi".
- Klitzing, Richard. "gaghi".
- Nan Ma. "Great grand 120-cell {5, 5/2, 3}".
- Wikipedia contributors. "Great grand 120-cell".
| truncations | ||||
|---|---|---|---|---|
| Name | OBSA | Schläfli symbol | CD diagram | Image |
| Great grand hecatonicosachoron | gaghi | {5,5/2,3} | | |
| Rectified great grand hecatonicosachoron | ragaghi | r{5,5/2,3} | |  |
| Rectified great faceted hexacosichoron | rigfix | r{3,5/2,5} | |  |
| Great faceted hexacosichoron | gofix | {3,5/2,5} | |  |
| Truncated great grand hecatonicosachoron | tigaghi | t{5,5/2,3} | |  |
| Small rhombated great grand hecatonicosachoron | sirgaghi | rr{5,5/2,3} | |  |
| Quasiprismatodishecatonicosachoron | quipdohi | t0,3{5,5/2,3} | | |
| (degenerate) | 2t{5,5/2,3} | | ||
| (degenerate) | rr{3,5/2,5} | | ||
| Truncated great faceted hexacosichoron | tigfix | t{3,5/2,5} | |  |
| (degenerate) | t0,1,2{5,5/2,3} | | ||
| (degenerate) | t0,1,3{5,5/2,3} | | ||
| Prismatorhombated great grand hecatonicosachoron | pirgaghi | t0,2,3{5,5/2,3} | |  |
| (degenerate) | t1,2,3{5,5/2,3} | | ||
| (degenerate) | t0,1,2,3{5,5/2,3} | | ||