| bgcolor=#e7dcc3 colspan=2 | Icosahedral 120-cell | |
|---|---|---|
| bgcolor=#ffffff align=center colspan=2 | Orthogonal projection | |
| Type | Schläfli-Hess polytope | |
| Cells | 120 | |
| Faces | 1200 | |
| Edges | 720 | |
| Vertices | 120 | |
| Vertex figure | ||
| Schläfli symbol | ||
| Symmetry group | H4, [3,3,5] | |
| Coxeter-Dynkin diagram | ||
| Dual | Small stellated 120-cell | |
| Properties | Regular |
It is constructed by 5 icosahedra around each edge in a pentagrammic figure. The vertex figure is a great dodecahedron.
It has the same edge arrangement as the 600-cell, grand 120-cell and great 120-cell, and shares its vertices with all other Schläfli–Hess 4-polytopes except the great grand stellated 120-cell (another stellation of the 120-cell).
As a faceted 600-cell, replacing the simplicial cells of the 600-cell with icosahedral pentagonal polytope cells, it could be seen as a four-dimensional analogue of the great dodecahedron, which replaces the triangular faces of the icosahedron with pentagonal faces. Indeed, the icosahedral 120-cell is dual to the small stellated 120-cell, which could be taken as a 4D analogue of the small stellated dodecahedron, dual of the great dodecahedron.