| bgcolor=#e7dcc3 colspan=2 | Grand 120-cell | |
|---|---|---|
| bgcolor=#ffffff align=center colspan=2 | Orthogonal projection | |
| Type | Schläfli-Hess polytope | |
| Cells | 120 | |
| Faces | 720 | |
| Edges | 720 | |
| Vertices | 120 | |
| Vertex figure | ||
| Schläfli symbol | ||
| Coxeter-Dynkin diagram | ||
| Symmetry group | H4, [3,3,5] | |
| Dual | Great stellated 120-cell | |
| Properties | Regular |
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.
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.