Great grand stellated 120-cell
Great grand stellated 120-cell | |
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Orthogonal projection
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Type | Schläfli-Hess polychoron
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Cells | 120 {5/2,3} |
Faces | 720 {5/2} |
Edges | 1200 |
Vertices | 600 |
Vertex figure | {3,3} |
Schläfli symbol | {5/2,3,3} |
Coxeter-Dynkin diagram |
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Symmetry group | H4, [3,3,5] |
Dual | Grand 600-cell |
Properties | Regular |
In
It is one of four regular star polychora discovered by
Images
H4 | A2 / B3 | A3 / B2 |
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Great grand stellated 120-cell, {5/2,3,3} | ||
[10] | [6] | [4] |
120-cell, {5,3,3} | ||
As a stellation
The great grand stellated 120-cell is the final stellation of the 120-cell, and is the only Schläfli-Hess polychoron to have the 120-cell for its convex hull. In this sense it is analogous to the three-dimensional great stellated dodecahedron, which is the final stellation of the dodecahedron and the only Kepler-Poinsot polyhedron to have the dodecahedron for its convex hull. Indeed, the great grand stellated 120-cell is dual to the grand 600-cell, which could be taken as a 4D analogue of the great icosahedron, dual of the great stellated dodecahedron.
The edges of the great grand stellated 120-cell are τ6 as long as those of the 120-cell core deep inside the polychoron, and they are τ3 as long as those of the small stellated 120-cell deep within the polychoron.
See also
- List of regular polytopes
- Convex regular 4-polytope– Set of convex regular polychora
- 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 [1].
- ISBN 0-486-61480-8.
- ISBN 978-1-56881-220-5(Chapter 26, Regular Star-polytopes, pp. 404–408)
- Klitzing, Richard. "4D uniform polytopes (polychora) o3o3o5/2x - gogishi".
External links
- Regular polychora Archived 2003-09-06 at the Wayback Machine
- Discussion on names
- Reguläre Polytope
- The Regular Star Polychora
- Zome Model of the Final Stellation of the 120-cell
Family | An | Bn | I2(p) / Dn | E6 / E7 / E8 / F4 / G2 | Hn
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Regular polygon | Triangle | Square | p-gon | Hexagon | Pentagon | |||||||
Uniform polyhedron | Tetrahedron | Octahedron • Cube | Demicube | Dodecahedron • Icosahedron | ||||||||
Uniform polychoron
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Pentachoron | 16-cell • Tesseract | Demitesseract | 24-cell | 120-cell • 600-cell | |||||||
Uniform 5-polytope | 5-simplex | 5-orthoplex • 5-cube | 5-demicube | |||||||||
Uniform 6-polytope | 6-simplex | 6-orthoplex • 6-cube | 6-demicube | 122 • 221 | ||||||||
Uniform 7-polytope | 7-simplex | 7-orthoplex • 7-cube | 7-demicube | 132 • 231 • 321 | ||||||||
Uniform 8-polytope | 8-simplex | 8-orthoplex • 8-cube | 8-demicube | 142 • 241 • 421 | ||||||||
Uniform 9-polytope | 9-simplex | 9-orthoplex • 9-cube | 9-demicube | |||||||||
Uniform 10-polytope | 10-simplex | 10-orthoplex • 10-cube | 10-demicube | |||||||||
Uniform n-polytope | n-simplex | n-orthoplex • n-cube | n-demicube | 1k2 • 2k1 • k21 | n-pentagonal polytope | |||||||
Topics: List of regular polytopes and compounds
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