Grand 120-cell
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| Grand 120-cell | |
|---|---|
 Orthogonal projection |
|
| Type | Schläfli-Hess polychoron |
| Cells | 120 {5,3} |
| Faces | 720 {5} |
| Edges | 720 |
| Vertices | 120 |
| Vertex figure | {3,5/2} |
| Schläfli symbol | {5,3,5/2} |
| Coxeter-Dynkin diagram |      |
| Symmetry group | H4, [3,3,5] |
| Dual | Great stellated 120-cell |
| Properties | -- |
In geometry, the grand 120-cell is a star polychoron with Schläfli symbol {5,3,5/2}. It is one of 10 regular Schläfli-Hess polychora.
It is one of four regular star polychora discovered by Ludwig Schläfli. It is named by John Horton Conway, extending the naming system by Arthur Cayley for the Kepler-Poinsot solids.
It has the same edge arrangement as the 600-cell, icosahedral 120-cell and the same face arrangement as the great 120-cell.
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[edit] References
- Edmund Hess, (1883) Einleitung in die Lehre von der Kugelteilung mit besonderer Berücksichtigung ihrer Anwendung auf die Theorie der Gleichflächigen und der gleicheckigen Polyeder [1].
- H. S. M. Coxeter, Regular Polytopes, 3rd. ed., Dover Publications, 1973. ISBN 0-486-61480-8.
[edit] See also
- List of regular polytopes
- Convex regular 4-polytope - Set of convex regular polychoron
- Kepler-Poinsot solids - regular star polyhedron
- Star polygon - regular star polygons
