600-cell
Sign in to saveAlso known as hexacosichoron, hexacosidedroid, tetraplex, tetrahedral complex, polytetrahedron
thumb|right|Net (polyhedron)|Net In geometry, the 600-cell is the convex regular 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol {3,3,5}. It is also known as the C600, hexacosichoron, hexacosihedroid and hypericosahedron. It is also called a tetraplex (abbreviated from "tetrahedral complex") and a polytetrahedron, being bounded by tetrahedral cells.
Key facts
- Polychoron.Name
- 600-cell
- Polychoron.Image_File
- Schlegel_wireframe_600-cell_vertex-centered.png
- Polychoron.Image_Caption
- Schlegel diagram, vertex-centered(vertices and edges)
- Polychoron.Type
- Convex regular 4-polytope
- Polychoron.Last
- 34
- Polychoron.Index
- 35
- Polychoron.Next
- 36
- Polychoron.Schläfli
- {3,3,5}
- Polychoron.Cell_List
- 600 ({3,3}) 20px
- Polychoron.Face_List
- 1200 {3}
- Polychoron.Edge_Count
- 720
- Polychoron.Vertex_Count
- 120
- Polychoron.Petrie_Polygon
- 30-gon
- Polychoron.Coxeter_Group
- H4, [3,3,5], order 14400
- Polychoron.Vertex_Figure
- 80pxicosahedron
- Polychoron.Dual
- 120-cell
- Polychoron.Property_List
- convex, isogonal, isotoxal, isohedral
via Wikipedia infobox
Wikidata facts
- Image
- 600-cell.gif
Show 2 more facts
- Schläfli symbol
- {3,3,5}
- Commons category
- 600-cell
Sources (2)
via Wikidata · CC0
~89 min read
Article
44 sectionsContents
- Geometry
- Coordinates
- Unit radius Cartesian coordinates
- Hopf spherical coordinates
- Structure
- Polyhedral sections
- Golden chords
- Boundary envelopes
- Geodesics
- Fibrations of great circle polygons
- Decagons
- Hexagons
- Squares
- Clifford parallel cell rings
- Constructions
- Gosset's construction
- Cell clusters
- Icosahedra
- Octahedra
- Union of two tori
- Boerdijk–Coxeter helix rings
- Radial golden triangles
- Characteristic orthoscheme
- Reflections
- Weyl orbits
- Rotations
- Twenty-five 24-cells
- Rotations on polygram isoclines
- Decagons and pentadecagrams
- Hexagons and hexagrams
- Squares and octagrams
- As a configuration
- Symmetries
- Visualization
- 2D projections
- 3D projections
- Animations
- Diminished 600-cells
- Related polytopes and honeycombs
- See also
- Notes
- Citations
- References
- External links
{{Infobox polychoron | Name=600-cell| Image_File=Schlegel_wireframe_600-cell_vertex-centered.png| Image_Caption=Schlegel diagram, vertex-centered(vertices and edges)| Type=Convex regular 4-polytope| Last=34| Index=35| Next=36| Schläfli={3,3,5}| CD=| Cell_List=600 ({3,3}) 20px| Face_List=1200 {3}| Edge_Count=720| Vertex_Count= 120| Petrie_Polygon=30-gon| Coxeter_Group=H4, [3,3,5], order 14400| Vertex_Figure=80pxicosahedron| Dual=120-cell| Property_List=convex, isogonal, isotoxal, isohedral }} thumb|right|Net (polyhedron)|Net In geometry, the 600-cell is the convex regular 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol {3,3,5}. It is also known as the C600, hexacosichoron, hexacosihedroid and hypericosahedron. It is also called a tetraplex (abbreviated from "tetrahedral complex") and a polytetrahedron, being bounded by tetrahedral cells.
The 600-cell's boundary is composed of 600 tetrahedral cells with 20 meeting at each vertex. Together they form 1200 triangular faces, 720 edges, and 120 vertices. It is the 4-dimensional analogue of the icosahedron, since it has five tetrahedra meeting at every edge, just as the icosahedron has five triangles meeting at every vertex. Its dual polytope is the 120-cell.