Grand stellated 120-cell
In geometry, the grand stellated 120-cell or grand stellated polydodecahedron is a regular star 4-polytope with Schläfli symbol {5/2,5,5/2}. It is one of 10 regular Schläfli-Hess polytopes. It is also one of two such polytopes that is self-dual.
| Grand stellated 120-cell | |
|---|---|
 Orthogonal projection | |
| Type | Schläfli-Hess polytope |
| Cells | 120 {5/2,5} |
| Faces | 720 {5/2} |
| Edges | 720 |
| Vertices | 120 |
| Vertex figure | {5,5/2} |
| Schläfli symbol | {5/2,5,5/2} |
| Coxeter-Dynkin diagram |      |
| Symmetry group | H4, [3,3,5] |
| Dual | self-dual |
| Properties | Regular |
Related polytopes
It has the same edge arrangement as the grand 600-cell, icosahedral 120-cell, and the same face arrangement as the great stellated 120-cell.
| H3 | A2 / B3 / D4 | A3 / B2 |
|---|---|---|
 |
 |
 |
Due to its self-duality, it does not have a good three-dimensional analogue, but (like all other star polyhedra and polychora) is analogous to the two-dimensional pentagram. With itself, it can form the compound of two grand stellated 120-cells.
See also
- List of regular polytopes
- Convex regular 4-polytope
- Kepler-Poinsot solids - regular star polyhedron
- Star polygon - regular star polygons
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 .
- H. S. M. Coxeter, Regular Polytopes, 3rd. ed., Dover Publications, 1973. ISBN 0-486-61480-8.
- John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, The Symmetries of Things 2008, ISBN 978-1-56881-220-5 (Chapter 26, Regular Star-polytopes, pp. 404–408)
- Klitzing, Richard. "4D uniform polytopes (polychora) x5/2o5o5/2o - gashi".
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