Grand stellated 120-cellOrthogonal projectionTypeSchläfli-Hess polytopeCells120 {5/2,5} Faces720 {5/2} Edges720Vertices120Vertex figure{5,5/2} Schläfli symbol {5/2,5,5/2}Coxeter-Dynkin diagramSymmetry groupH4, [3,3,5]Dualself-dualProperties Regular
In geometry, the grand stellated 120-cell or grand stellated polydodecahedron is a regular star 4-polytope with Schläfli symbol {5/2,5,5/2}. It is one of 10 regular Schläfli-Hess polytopes. It is also one of two such polytopes that is self-dual.
Related polytopes
The grand stellated 120-cell has the same edge arrangement as the great icosahedral 120-cell and grand 600-cell, and also the same face arrangement as the great stellated 120-cell.
+ Orthographic projections by Coxeter planesH3A2 / 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