Icosahedral 120-cell
| Icosahedral 120-cell | |
|---|---|
 Orthogonal projection | |
| Type | Schläfli-Hess polychoron |
| Cells | 120 {3,5} |
| Faces | 1200 {3} |
| Edges | 720 |
| Vertices | 120 |
| Vertex figure | {5,5/2} |
| Schläfli symbol | {3,5,5/2} |
| Symmetry group | H4, [3,3,5] |
| Coxeter-Dynkin diagram |      
|
| Dual | Small stellated 120-cell |
| Properties | -- |
In geometry, the icosahedral 120-cell is a star polychoron with Schläfli symbol {3,5,5/2}. It is one of 10 regular Schläfli-Hess polychora.
It is constructed by 5 icosahedra around each edge in a pentagrammic figure. The vertex figure is a great dodecahedron.
Related polytopes
It has the same edge arrangement as the 600-cell, grand 120-cell and great 120-cell, and shares its vertices with each other Schlaffi-Hess Polychoron, besides the Great grand stellated 120-cell, another stellation of the Hecatonicosachoron. File:IcosahedralHecatonicosa.png
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 [1].
- 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)
See also
- List of regular polytopes
- Convex regular 4-polytope - Set of convex regular polychoron
- Kepler-Poinsot solids - regular star polyhedron
- Star polygon - regular star polygons
External links
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