cross-polytope
Sign in to saveAlso known as orthoplex, hyperoctahedron, cocube
{| 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 |}
Wikidata facts
- Instance of
- polytope family
- Image
- Schlegel wireframe 16-cell.png
Show 5 more facts
- Commons category
- Cross-polytope graphs
- Schläfli symbol
- {3ⁿ⁻²,4}
- dual to
- hypercube
- studied by
- solid geometry
- maintained by WikiProject
- WikiProject Mathematics
Sources (1)
via Wikidata · CC0
~9 min read
Encyclopedic overview
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.
Excerpted from Wikipedia’s “cross-polytope” article, available under the CC BY-SA 4.0 licence.