Small stellated 120-cellOrthogonal projectionTypeSchläfli-Hess polytopeCells120 {5/2,5} Faces720 {5/2} Edges1200Vertices120Vertex figure{5,3} Schläfli symbol {5/2,5,3}Coxeter-Dynkin diagramSymmetry groupH4, [3,3,5]Dual Icosahedral 120-cellProperties Regular In geometry, the small stellated 120-cell or stellated polydodecahedron is a regular star 4-polytope with Schläfli symbol {5/2,5,3}. It is one of 10 regular Schläfli-Hess polytopes.
Related polytopes
It has the same edge arrangement as the great grand 120-cell, and also shares its 120 vertices with the 600-cell and eight other regular star 4-polytopes. It may also be seen as the first stellation of the 120-cell. In this sense it could be seen as analogous to the three-dimensional small stellated dodecahedron, which is the first stellation of the dodecahedron. Indeed, the small stellated 120-cell is dual to the icosahedral 120-cell, which could be taken as a 4D analogue of the great dodecahedron, dual of the small stellated dodecahedron.
The edges of the small stellated 120-cell are τ2 as long as those of the 120-cell core inside the 4-polytope. + Orthographic projections by Coxeter planesH3A2 / B3 / D4A3 / B2
See also List of regular polytopes Convex regular 4-polytope - Set of 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 Zome Model of the Final Stellation of the 120-cell The First Stellation of the 120-cell, A Zome Model