tesseract
Sign in to saveAlso known as 8-cell, cubic prism, 4-cube, octachoron, octahedroid, 4-hypercube
In geometry, a tesseract or 4-cube is a four-dimensional hypercube, analogous to a two-dimensional square and a three-dimensional cube. Just as the perimeter of the square consists of four edges and the surface of the cube consists of six square faces, the hypersurface of the tesseract consists of eight cubical cells, meeting at right angles. The tesseract is one of the six convex regular 4-polytopes.
Key facts
- Polychoron.Name
- Tesseract8-cell(4-cube)
- Polychoron.Image_File
- 8-cell-simple.gif
- Polychoron.Type
- Convex regular 4-polytope
- Polychoron.Family
- Hypercubes
- Polychoron.Last
- 9
- Polychoron.Index
- 10
- Polychoron.Next
- 11
- Polychoron.Schläfli
- {4,3,3}t0,3{4,3,2} or {4,3}×{ }t0,2{4,2,4} or {4}×{4}t0,2,3{4,2,2} or {4}×{ }×{ }t0,1,2,3{2,2,2} or { }×{ }×{ }×{ }
- Polychoron.Cell_List
- 8 {4,3} 20px
- Polychoron.Face_List
- 24 {4}
- Polychoron.Edge_Count
- 32
- Polychoron.Vertex_Count
- 16
- Polychoron.Petrie_Polygon
- octagon
- Polychoron.Coxeter_Group
- B4, [3,3,4]
- Polychoron.Vertex_Figure
- 80px|class=skin-invertTetrahedron
- Polychoron.Dual
- 16-cell
- Polychoron.Property_List
- convex, isogonal, isotoxal, isohedral, Hanner polytope
via Wikipedia infobox
Wikidata facts
- Image
- 8-cell-simple.gif
Show 3 more facts
- Commons category
- Tesseract
- described at URL
- www.youtube.com/watch?v=UnURElCzGc0
- Schläfli symbol
- {4,3,3}
Sources (3)
via Wikidata · CC0
~16 min read
Article
14 sectionsContents
- Construction
- In popular cultures
- Properties
- Unit tesseract
- Radial equilateral symmetry
- Formulas
- As a configuration
- Projections
- Tessellation
- Related polytopes and honeycombs
- Notes
- References
- Sources
- External links
{{Infobox polychoron | Name=Tesseract8-cell(4-cube) | Image_File=8-cell-simple.gif | Type=Convex regular 4-polytope | Family=Hypercubes | Last=9 | Index=10 | Next=11 | Schläfli={4,3,3}t0,3{4,3,2} or {4,3}×{ }t0,2{4,2,4} or {4}×{4}t0,2,3{4,2,2} or {4}×{ }×{ }t0,1,2,3{2,2,2} or { }×{ }×{ }×{ } | CD= | Cell_List=8 {4,3} 20px | Face_List=24 {4} | Edge_Count=32 | Vertex_Count=16 | Petrie_Polygon=octagon | Coxeter_Group=B4, [3,3,4] | Vertex_Figure=80px|class=skin-invertTetrahedron | Dual=16-cell | Property_List=convex, isogonal, isotoxal, isohedral, Hanner polytope }} In geometry, a tesseract or 4-cube is a four-dimensional hypercube, analogous to a two-dimensional square and a three-dimensional cube. Just as the perimeter of the square consists of four edges and the surface of the cube consists of six square faces, the hypersurface of the tesseract consists of eight cubical cells, meeting at right angles. The tesseract is one of the six convex regular 4-polytopes.
The tesseract is also called an 8-cell, C8, (regular) octachoron, or cubic prism. It is the four-dimensional measure polytope, taken as a unit for hypervolume. Harold Scott MacDonald Coxeter labels it the polytope. The term hypercube without a dimension reference is frequently treated as a synonym for this specific polytope.