Grand 120-cellOrthogonal projectionTypeSchläfli-Hess polytopeCells120 {5,3} Faces720 {5} Edges720Vertices120Vertex figure{3,5/2} Schläfli symbol {5,3,5/2}Coxeter-Dynkin diagramSymmetry groupH4, [3,3,5]Dual Great stellated 120-cellProperties Regular In geometry, the grand 120-cell or grand polydodecahedron is a regular star 4-polytope with Schläfli symbol {5,3,5/2}. It is one of 10 regular Schläfli-Hess polytopes.
It is one of four regular star 4-polytopes discovered by Ludwig Schläfli. It is named by John Horton Conway, extending the naming system by Arthur Cayley for the Kepler-Poinsot solids.
Related polytopes It has the same edge arrangement as the 600-cell, icosahedral 120-cell and the same face arrangement as the great 120-cell. + Orthographic projections by Coxeter planesH4 -F4H3A2 / B3 / D4A3 / B2 It could be seen as another 4D analogue of the three-dimensional great dodecahedron due to being a pentagonal polytope with enlarged facets.
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