Great 120-cell explained
| bgcolor=#e7dcc3 colspan=2 | Great 120-cell |
|---|
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Orthogonal projection |
| Type | Schläfli-Hess polytope |
| Cells | 120 |
| Faces | 720 |
| Edges | 720 |
| Vertices | 120 |
| Vertex figure | |
| Schläfli symbol | |
| Coxeter-Dynkin diagram | |
| Symmetry group | H4, [3,3,5] |
| Dual | self-dual |
| Properties | Regular | |
In
geometry, the
great 120-cell or
great polydodecahedron is a regular star 4-polytope with
Schläfli symbol . It is one of 10 regular Schläfli-Hess polytopes. It is one of the two such polytopes that is self-dual.
Related polytopes
It has the same edge arrangement as the 600-cell, icosahedral 120-cell as well as the same face arrangement as the grand 120-cell.
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.
See also
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 http://www.hti.umich.edu/cgi/b/bib/bibperm?q1=ABN8623.0001.001.
- H. S. M. Coxeter, Regular Polytopes, 3rd. ed., Dover Publications, 1973. .
- John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things 2008, (Chapter 26, Regular Star-polytopes, pp. 404 - 408)
External links
