| bgcolor=#e7dcc3 colspan=2 | Great grand stellated 120-cell | |
|---|---|---|
| bgcolor=#ffffff align=center colspan=2 | Orthogonal projection | |
| Type | Schläfli-Hess polychoron | |
| Cells | 120 | |
| Faces | 720 | |
| Edges | 1200 | |
| Vertices | 600 | |
| Vertex figure | ||
| Schläfli symbol | ||
| Coxeter-Dynkin diagram | ||
| Symmetry group | H4, [3,3,5] | |
| Dual | Grand 600-cell | |
| Properties | Regular |
It is one of four regular star polychora discovered by Ludwig Schläfli. It is named by John Horton Conway, extending the naming system by Arthur Cayley for the Kepler-Poinsot solids, and the only one containing all three modifiers in the name.
The great grand stellated 120-cell is the final stellation of the 120-cell, and is the only Schläfli-Hess polychoron to have the 120-cell for its convex hull. In this sense it is analogous to the three-dimensional great stellated dodecahedron, which is the final stellation of the dodecahedron and the only Kepler-Poinsot polyhedron to have the dodecahedron for its convex hull. Indeed, the great grand stellated 120-cell is dual to the grand 600-cell, which could be taken as a 4D analogue of the great icosahedron, dual of the great stellated dodecahedron.
The edges of the great grand stellated 120-cell are τ6 as long as those of the 120-cell core deep inside the polychoron, and they are τ3 as long as those of the small stellated 120-cell deep within the polychoron.