Great faceted hexacosichoron
|Great faceted hexacosichoron|
|Bowers style acronym||Gofix|
|Coxeter diagram||o5o5/2o3x ()|
|Cells||120 great icosahedra|
|Vertex figure||Small stellated dodecahedron, edge length 1|
|Edge figure||gike 3 gike 3 gike 3 gike 3 gike 3|
|Measures (edge length 1)|
|Number of external pieces||7200|
|Level of complexity||12|
|Army||Ex, edge length|
|Dual||Great grand hecatonicosachoron|
|Abstract & topological properties|
|Symmetry||H4, order 14400|
The great faceted hexacosichoron, or gofix, also commonly called the great icosahedral 120-cell, is one of the 10 regular Schläfli–Hess polychora. It has 120 great icosahedra as cells, joining 5 to an edge and 12 to a vertex in the form of a small stellated dodecahedron.
The great faceted hexacosichoron is a faceting of the great stellated hecatonicosachoron, sharing its vertices and edges. The cells are in the same planes as the small stellated dodecahedra of the grand stellated hecatonicosachoron.
Cross-sections[edit | edit source]
Vertex coordinates[edit | edit source]
Its vertices are the same as those of its regiment colonel, the great stellated hecatonicosachoron.
Related polychora[edit | edit source]
The great faceted hexacosichoron is the captain of a company in the regiment of the great stellated hecatonicosachoron, having the same faces as the grand hexacosichoron.
Uniform polychoron compounds composed of faceted hexacosichora include:
- Great faceted chirotetrahedral dishexacosichoron (2)
- Great faceted snub pentishecatonicosachoron (5)
- Great chiricosahedral hyperprismatochoron (6)
- Great faceted snub decahecatonicosachoron (10)
- Great disicosahedral hyperprismatochoron (12)
External links[edit | edit source]
- Bowers, Jonathan. "Category 1: Regular Polychora" (#14).
- Klitzing, Richard. "gofix".
- Wikipedia Contributors. "Great icosahedral 120-cell".