| bgcolor=#e7dcc3 colspan=2 | Small stellated 120-cell | |
|---|---|---|
| bgcolor=#ffffff align=center colspan=2 | Orthogonal projection | |
| Type | Schläfli-Hess polytope | |
| Cells | 120 | |
| Faces | 720 | |
| Edges | 1200 | |
| Vertices | 120 | |
| Vertex figure | ||
| Schläfli symbol | ||
| Coxeter-Dynkin diagram | ||
| Symmetry group | H4, [3,3,5] | |
| Dual | Icosahedral 120-cell | |
| Properties | Regular |
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.