120-cell
Sign in to savethumb|right|Net (polyhedron)|Net 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.
Key facts
- Polychoron.Name
- 120-cell
- Polychoron.Image_File
- Schlegel wireframe 120-cell.png
- Polychoron.Image_Caption
- Schlegel diagram(vertices and edges)
- Polychoron.Type
- Convex regular 4-polytope
- Polychoron.Last
- 31
- Polychoron.Index
- 32
- Polychoron.Next
- 33
- Polychoron.Schläfli
- {5,3,3}
- Polychoron.Cell_List
- 120 {5,3} 20px
- Polychoron.Face_List
- 720 {5} 20px
- Polychoron.Edge_Count
- 1200
- Polychoron.Vertex_Count
- 600
- Polychoron.Petrie_Polygon
- 30-gon
- Polychoron.Coxeter_Group
- H4, [3,3,5]
- Polychoron.Vertex_Figure
- 80pxtetrahedron
- Polychoron.Dual
- 600-cell
- Polychoron.Property_List
- convex, isogonal, isotoxal, isohedral
via Wikipedia infobox
Article
34 sectionsContents
- Geometry
- Cartesian coordinates
- √8 radius coordinates
- Unit radius coordinates
- Chords
- Relationships among interior polytopes
- Compound of five 600-cells
- Geodesic rectangles
- Concentric hulls
- Polyhedral graph
- Constructions
- Dual 600-cells
- Cell rotations of inscribed duals
- Augmentation
- Weyl orbits
- As a configuration
- Visualization
- Layered stereographic projection
- Intertwining rings
- Other great circle constructs
- 2D Orthogonal projections
- 3D Perspective projections
- Animations
- Related polyhedra and honeycombs
- H<sub>4</sub> polytopes
- {p,3,3} polytopes
- {5,3,p} polytopes
- Tetrahedrally diminished 120-cell
- Davis 120-cell manifold
- See also
- Notes
- Citations
- References
- External links
{{Infobox polychoron | Name=120-cell | Image_File=Schlegel wireframe 120-cell.png | Image_Caption=Schlegel diagram(vertices and edges) | Type=Convex regular 4-polytope | Last=31 | Index=32 | Next=33 | Schläfli={5,3,3}| CD=| Cell_List=120 {5,3} 20px| Face_List=720 {5} 20px| Edge_Count=1200| Vertex_Count= 600| Petrie_Polygon=30-gon| Coxeter_Group=H4, [3,3,5]| Vertex_Figure=80pxtetrahedron| Dual=600-cell| Property_List=convex, isogonal, isotoxal, isohedral }} thumb|right|Net (polyhedron)|Net 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.