Great 120-cellOrthogonal projectionTypeSchläfli-Hess polytopeCells120 {5,5/2} Faces720 {5} Edges720Vertices120Vertex figure{5/2,5} Schläfli symbol {5,5/2,5}Coxeter-Dynkin diagramSymmetry groupH4, [3,3,5]Dualself-dualProperties Regular
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.
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. + Orthographic projections by Coxeter planesH4 -F4H3A2 / B3 / D4A3 / B2
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 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. . John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things 2008, (Chapter 26, Regular Star-polytopes, pp. 404–408)
External links Regular polychora Discussion on names Reguläre Polytope The Regular Star Polychora