Great 120-cell
In geometry, the great 120-cell or great polydodecahedron is a regular star 4-polytope with Schläfli symbol {5,5/2,5}. It is one of 10 regular Schläfli-Hess polytopes. It is one of the two such polytopes that is self-dual.
Great 120-cell | |
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![]() Orthogonal projection | |
Type | Schläfli-Hess polytope |
Cells | 120 {5,5/2} |
Faces | 720 {5} |
Edges | 720 |
Vertices | 120 |
Vertex figure | {5/2,5} |
Schläfli symbol | {5,5/2,5} |
Coxeter-Dynkin diagram | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Symmetry group | H4, [3,3,5] |
Dual | self-dual |
Properties | Regular |
![](../I/Schl%C3%A4fli-Hess_polychoron-wireframe-3.png.webp)
Orthogonal projection as a wireframe
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.
H4 | - | F4 |
---|---|---|
![]() [30] |
![]() [20] |
![]() [12] |
H3 | A2 / B3 / D4 | A3 / B2 |
![]() [10] |
![]() [6] |
![]() [4] |
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 great 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) o5o5/2o5x - gohi".
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