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.
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 [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) x5/2o5o5/2o - gashi".
External links Regular polychora Archived 2003-09-06 at the Wayback Machine Discussion on names Reguläre Polytope The Regular Star Polychora