| 释义 |
- Related polytopes
- See also
- References
- External links
| Grand 120-cell |
Orthogonal projection | | Type | Schläfli-Hess polytope | | 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 | node_1|5|node|3|node | d2|node} | | Symmetry group | H4, [3,3,5] | | Dual | Great stellated 120-cell | | Properties | Regular |
In geometry, the grand 120-cell or grand polydodecahedron is a regular star 4-polytope with Schläfli symbol {5,3,5/2}. It is one of 10 regular Schläfli-Hess polytopes. It is one of four regular star 4-polytopes discovered by Ludwig Schläfli. It is named by John Horton Conway, extending the naming system by Arthur Cayley for the Kepler-Poinsot solids. Related polytopesIt has the same edge arrangement as the 600-cell, icosahedral 120-cell and the same face arrangement as the great 120-cell. Orthographic projections by Coxeter planes| H4 | - | F4 |
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[30] |
[20] |
[12] | | H3 | A2 / B3 / D4 | A3 / B2 |
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[10] |
[6] |
[4] | With its dual, it forms the compound of grand 120-cell and great stellated 120-cell. 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)|o5o3o5/2x - gahi}}
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]
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