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.
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 [1]. 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) Klitzing, Richard. "4D uniform polytopes (polychora) o5o3o5/2x - gahi".
External links Regular polychora Archived 2003-09-06 at the Wayback Machine Discussion on names Reguläre Polytope The Regular Star Polychora