| Small stellated 120-cell | |
|---|---|
 Orthogonal projection | |
| Type | Schläfli-Hess polytope |
| Cells | 120 {5/2,5} |
| Faces | 720 {5/2} |
| Edges | 1200 |
| Vertices | 120 |
| Vertex figure | {5,3} |
| Schläfli symbol | {5/2,5,3} |
| Coxeter-Dynkin diagram |       |
| Symmetry group | H4, [3,3,5] |
| Dual | Icosahedral 120-cell |
| Properties | Regular |
In geometry, the small stellated 120-cell or stellated polydodecahedron is a regular star 4-polytope with Schläfli symbol {5/2,5,3}. It is one of 10 regular Schläfli-Hess polytopes.
Related polytopes
It has the same edge arrangement as the great grand 120-cell, and also shares its 120 vertices with the 600-cell and eight other regular star 4-polytopes. It may also be seen as the first stellation of the 120-cell. In this sense it could be seen as analogous to the three-dimensional small stellated dodecahedron, which is the first stellation of the dodecahedron. Indeed, the small stellated 120-cell is dual to the icosahedral 120-cell, which could be taken as a 4D analogue of the great dodecahedron, dual of the small stellated dodecahedron.
The edges of the small stellated 120-cell are τ2 as long as those of the 120-cell core inside the 4-polytope.
| H3 | A2 / B3 / D4 | A3 / B2 |
|---|---|---|
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 |
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See also
- List of regular polytopes
- Convex regular 4-polytope - Set of 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) o3o5o5/2x - sishi".