great icosahedral 120-cell
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!bgcolor=#e7dcc3 colspan=2|Great icosahedral 120-cell | |
| bgcolor=#ffffff align=center colspan=2|280px Orthogonal projection | |
| bgcolor=#e7dcc3|Type | Schläfli-Hess polytope |
| bgcolor=#e7dcc3|Cells | 120 {3,5/2} |
| bgcolor=#e7dcc3|Faces | 1200 {3} |
| bgcolor=#e7dcc3|Edges | 720 |
| bgcolor=#e7dcc3|Vertices | 120 |
| bgcolor=#e7dcc3|Vertex figure | {5/2,5} |
| bgcolor=#e7dcc3|Schläfli symbol | {3,5/2,5} |
| bgcolor=#e7dcc3|Coxeter-Dynkin diagram | {{CDD|node_1|3|node|5|rat|d2|node|5|node}} |
| bgcolor=#e7dcc3|Symmetry group | H4, [3,3,5] |
| bgcolor=#e7dcc3|Dual | Great grand 120-cell |
| bgcolor=#e7dcc3|Properties | Regular |
In geometry, the great icosahedral 120-cell, great polyicosahedron or great faceted 600-cell is a regular star 4-polytope with Schläfli symbol {3,5/2,5}. It is one of 10 regular Schläfli-Hess polytopes.
Related polytopes
It has the same edge arrangement as the great stellated 120-cell, and grand stellated 120-cell, and face arrangement of the grand 600-cell.
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|+ Orthographic projections by Coxeter planes |
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!H3 !A2 / B3 / D4 !A3 / B2 |
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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 [http://www.hti.umich.edu/cgi/b/bib/bibperm?q1=ABN8623.0001.001].
- H. S. M. Coxeter, Regular Polytopes, 3rd. ed., Dover Publications, 1973. {{ISBN|0-486-61480-8}}.
- John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, 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)|x3o5/2o5o - gofix}}
External links
- [http://hometown.aol.com/hedrondude/regulars.html Regular polychora] {{Webarchive|url=https://web.archive.org/web/20030906012615/http://hometown.aol.com/hedrondude/regulars.html |date=2003-09-06 }}
- [http://mathforum.org/library/drmath/view/54786.html 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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