4-polytope
Sign in to saveAlso known as polyhedroid, polycell
{|class=wikitable style="float:right; margin-left:8px" |+ Graphs of the six convex regular 4-polytopes |- !{3,3,3} !{3,3,4} !{4,3,3} |- valign=top align=center |120px5-cellPentatope4-simplex |121px16-cellOrthoplex4-orthoplex |120px8-cellTesseract4-cube |- !{3,4,3} !{3,3,5} !{5,3,3} |- valign=top align=center |120px24-cellOctaplex |120px600-cellTetraplex |120px120-cellDodecaplex |}
~12 min read
Article
12 sectionsContents
- Definition
- Geometry
- Visualisation
- Topological characteristics
- Classification
- Criteria
- Classes
- See also
- References
- Notes
- Bibliography
- External links
{|class=wikitable style="float:right; margin-left:8px" |+ Graphs of the six convex regular 4-polytopes |- !{3,3,3} !{3,3,4} !{4,3,3} |- valign=top align=center |120px5-cellPentatope4-simplex |121px16-cellOrthoplex4-orthoplex |120px8-cellTesseract4-cube |- !{3,4,3} !{3,3,5} !{5,3,3} |- valign=top align=center |120px24-cellOctaplex |120px600-cellTetraplex |120px120-cellDodecaplex |}
In geometry, a 4-polytope (sometimes also called a polychoron, polycell, or polyhedroid) is a four-dimensional polytope. It is a connected and closed figure, composed of lower-dimensional polytopal elements: vertices, edges, faces (polygons), and cells (polyhedra). Each face is shared by exactly two cells. The 4-polytopes were discovered by the Swiss mathematician Ludwig Schläfli before 1853.