120-cell
| 120-cell | |
|---|---|
Schlegel diagram (vertices and edges) | |
| Type | Convex regular 4-polytope |
| Schläfli symbol | {5,3,3} |
| Coxeter diagram | |
| Cells | 120 {5,3} |
| Faces | 720 {5} |
| Edges | 1200 |
| Vertices | 600 |
| Vertex figure | tetrahedron |
| Petrie polygon | 30-gon |
| Coxeter group | H4, [3,3,5] |
| Dual | 600-cell |
| Properties | convex, isogonal, isotoxal, isohedral |
| Uniform index | 32 |
In geometry, the 120-cell is the convex regular 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol {5,3,3}. It is also called a C120, dodecaplex (short for "dodecahedral complex"), hyperdodecahedron, polydodecahedron, hecatonicosachoron, dodecacontachoron and hecatonicosahedroid.
The boundary of the 120-cell is composed of 120 dodecahedral cells with 4 meeting at each vertex. Together they form 720 pentagonal faces, 1200 edges, and 600 vertices. It is the 4-dimensional analogue of the regular dodecahedron, since just as a dodecahedron has 12 pentagonal facets, with 3 around each vertex, the dodecaplex has 120 dodecahedral facets, with 3 around each edge. Its dual polytope is the 600-cell.