16-cell
Sign in to saveAlso known as hexadecachoron, 4-orthoplex, tetracross, demitesseract, 4-demicube, hexdecahedroid
In geometry, the 16-cell is the regular convex 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol {3,3,4}. It is one of the six regular convex 4-polytopes first described by the Swiss mathematician Ludwig Schläfli in the mid-19th century. It is also called C16, hexadecachoron, or hexdecahedroid.
Key facts
- Polychoron.Name
- 16-cell(4-orthoplex)
- Polychoron.Image_File
- Schlegel wireframe 16-cell.png
- Polychoron.Image_Caption
- Schlegel diagram(vertices and edges)
- Polychoron.Type
- Convex regular 4-polytope4-orthoplex4-demicube
- Polychoron.Last
- 11
- Polychoron.Index
- 12
- Polychoron.Next
- 13
- Polychoron.Schläfli
- {3,3,4}
- Polychoron.Cell_List
- 16 {3,3} 25px
- Polychoron.Face_List
- 32 {3} 25px
- Polychoron.Edge_Count
- 24
- Polychoron.Vertex_Count
- 8
- Polychoron.Petrie_Polygon
- octagon
- Polychoron.Coxeter_Group
- B4, [3,3,4], order 384D4, order 192
- Polychoron.Vertex_Figure
- 80pxOctahedron
- Polychoron.Dual
- Tesseract
- Polychoron.Property_List
- convex, isogonal, isotoxal, isohedral, regular, Hanner polytope
via Wikipedia infobox
Wikidata facts
- Image
- 4-orthoplex.svg
Show 2 more facts
- Schläfli symbol
- {3,3,4}
- Commons category
- 16-cell
Sources (2)
via Wikidata · CC0
~28 min read
Article
20 sectionsContents
- Geometry
- Coordinates
- Structure
- Rotations
- Constructions
- Octahedral dipyramid
- Tetrahedral constructions
- Helical construction
- As a configuration
- Tessellations
- Projections
- 4 sphere Venn diagram
- Symmetry constructions
- Related complex polygons
- Related uniform polytopes and honeycombs
- See also
- Notes
- Citations
- References
- External links
{{Infobox polychoron | Name=16-cell(4-orthoplex)| Image_File=Schlegel wireframe 16-cell.png| Image_Caption=Schlegel diagram(vertices and edges)| Type=Convex regular 4-polytope4-orthoplex4-demicube| Last=11| Index=12| Next=13| Schläfli={3,3,4}| CD= | Cell_List=16 {3,3} 25px| Face_List=32 {3} 25px| Edge_Count= 24| Vertex_Count= 8| Petrie_Polygon=octagon| Coxeter_Group=B4, [3,3,4], order 384D4, order 192| Vertex_Figure=80pxOctahedron| Dual=Tesseract| Property_List=convex, isogonal, isotoxal, isohedral, regular, Hanner polytope }} In geometry, the 16-cell is the regular convex 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol {3,3,4}. It is one of the six regular convex 4-polytopes first described by the Swiss mathematician Ludwig Schläfli in the mid-19th century. It is also called C16, hexadecachoron, or hexdecahedroid.
It is the 4-dimensional member of an infinite family of polytopes called cross-polytopes, orthoplexes, or hyperoctahedrons which are analogous to the octahedron in three dimensions. It is Coxeter's \beta_4 polytope. The dual polytope is the tesseract (4-cube), which it can be combined with to form a compound figure. The cells of the 16-cell are dual to the 16 vertices of the tesseract.