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| 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[1] and hecatonicosahedroid.[2]
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.[a] Its dual polytope is the 600-cell.
- ^ N.W. Johnson: Geometries and Transformations, (2018) ISBN 978-1-107-10340-5 Chapter 11: Finite Symmetry Groups, 11.5 Spherical Coxeter groups, p.249
- ^ Matila Ghyka, The Geometry of Art and Life (1977), p.68
- ^ Coxeter 1973, pp. 292–293, Table I(ii); "120-cell".
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