| 释义 |
- Related polytopes
- See also
- References
- External links
| 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 | node_1|5|rat|d2|node|5|node|5|rat|d2|node}} | | Symmetry group | H4, [3,3,5] | | Dual | self-dual | | Properties | Regular |
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. 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. Orthographic projections by Coxeter planes| H3 | A2 / B3 / D4 | A3 / B2 |
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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)
- {{KlitzingPolytopes|polychora.htm|4D uniform polytopes (polychora)|x5/2o5o5/2o - gashi}}
External links - Regular polychora
- Discussion on names
- [https://web.archive.org/web/20061107052613/http://www.mathematik.uni-regensburg.de/Goette/sterne/ Reguläre Polytope]
- [https://web.archive.org/web/20070704012333/http://davidf.faricy.net/polyhedra/Star_Polychora.html The Regular Star Polychora]
{{Regular 4-polytopes}}{{polychora-stub}} 1 : Polychora |