cross-polytope
Sign in to save{| class="wikitable floatright" |+ Cross-polytopes of dimension 2 to 5 |- |style="text-align: center;"|120px|A 2-dimensional cross-polytope |style="text-align: center;"|120px|A 3-dimensional cross-polytope |- |style="text-align: center;"|2 dimensionssquare |style="text-align: center;"|3 dimensionsoctahedron |- |style="text-align: center;"|120px|A 4-dimensional cross-polytope |style="text-align: center;"|120px|A 5-dimensional cross-polytope |- |style="text-align: center;"|4 dimensions16-cell |style="text-align: center;"|5 dimensions5-orthoplex |}
Article
8 sectionsContents
- Low-dimensional examples
- ''n'' dimensions
- Generalized orthoplex
- Related polytope families
- See also
- Citations
- References
- External links
{| class="wikitable floatright" |+ Cross-polytopes of dimension 2 to 5 |- |style="text-align: center;"|120px|A 2-dimensional cross-polytope |style="text-align: center;"|120px|A 3-dimensional cross-polytope |- |style="text-align: center;"|2 dimensionssquare |style="text-align: center;"|3 dimensionsoctahedron |- |style="text-align: center;"|120px|A 4-dimensional cross-polytope |style="text-align: center;"|120px|A 5-dimensional cross-polytope |- |style="text-align: center;"|4 dimensions16-cell |style="text-align: center;"|5 dimensions5-orthoplex |}
In geometry, a cross-polytope, hyperoctahedron, orthoplex, staurotope, or cocube is a regular, convex polytope that exists in n-dimensional Euclidean space. A 2-dimensional cross-polytope is a square, a 3-dimensional cross-polytope is a regular octahedron, and a 4-dimensional cross-polytope is a 16-cell. Its facets are simplexes of the previous dimension, while the cross-polytope's vertex figure is another cross-polytope from the previous dimension.