Grand 600-cell
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| Grand 600-cell | |
|---|---|
 Orthogonal projection |
|
| Type | Schläfli-Hess polychoron |
| Cells | 600 {3,3} |
| Faces | 1200 {3} |
| Edges | 720 |
| Vertices | 120 |
| Vertex figure | {3,5/2} |
| Schläfli symbol | {3,3,5/2} |
| Coxeter-Dynkin diagram |     |
| Symmetry group | H4, [3,3,5] |
| Dual | Great grand stellated 120-cell |
| Properties | -- |
In geometry, the Grand 600-cell is a star polychoron with Schläfli symbol {3,3,5/2}. It is one of 10 regular Schläfli-Hess polychora. It is the only one with 600 cells.
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 great stellated 120-cell, and grand stellated 120-cell, and same face arrangement as the great icosahedral 120-cell.
[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
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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.
