17 relations: Cross-polytope, E9 honeycomb, Gosset–Elte figures, Hexadecagon, List of mathematical shapes, List of polygons, polyhedra and polytopes, List of regular polytopes and compounds, Nine-dimensional space, Octadecagon, Polytope families, Rectified 9-cubes, Rectified 9-orthoplexes, Uniform 9-polytope, Uniform k 21 polytope, 10-orthoplex, 8-simplex, 9-cube.
In geometry, a cross-polytope, orthoplex, hyperoctahedron, or cocube is a regular, convex polytope that exists in n-dimensions.
In geometry, an E9 honeycomb is a tessellation of uniform polytopes in hyperbolic 9-dimensional space.
In geometry, the Gosset–Elte figures, named by Coxeter after Thorold Gosset and E. L. Elte, are a group of uniform polytopes which are not regular, generated by a Wythoff construction with mirrors all related by order-2 and order-3 dihedral angles.
In mathematics, a hexadecagon (sometimes called a hexakaidecagon) or 16-gon is a sixteen-sided polygon.
Following is a list of some mathematically well-defined shapes.
A polytope is a geometric object with flat sides, which exists in any general number of dimensions.
This page lists the regular polytopes and regular polytope compounds in Euclidean, spherical and hyperbolic spaces.
In mathematics, a sequence of n real numbers can be understood as a point in n-dimensional space.
An octadecagon (or octakaidecagon) or 18-gon is an eighteen-sided polygon.
There are several families of symmetric polytopes with irreducible symmetry which have a member in more than one dimensionality.
In nine-dimensional geometry, a rectified 9-cube is a convex uniform 9-polytope, being a rectification of the regular 9-cube.
In nine-dimensional geometry, a rectified 9-simplex is a convex uniform 9-polytope, being a rectification of the regular 9-orthoplex.
In nine-dimensional geometry, a nine-dimensional polytope or 9-polytope is a polytope contained by 8-polytope facets.
In geometry, a uniform k21 polytope is a polytope in k + 4 dimensions constructed from the ''E''''n'' Coxeter group, and having only regular polytope facets.
In geometry, a 10-orthoplex or 10-cross polytope, is a regular 10-polytope with 20 vertices, 180 edges, 960 triangle faces, 3360 octahedron cells, 8064 5-cells 4-faces, 13440 5-faces, 15360 6-faces, 11520 7-faces, 5120 8-faces, and 1024 9-faces.
In geometry, an 8-simplex is a self-dual regular 8-polytope.
In geometry, a 9-cube is a nine-dimensional hypercube with 512 vertices, 2304 edges, 4608 square faces, 5376 cubic cells, 4032 tesseract 4-faces, 2016 5-cube 5-faces, 672 6-cube 6-faces, 144 7-cube 7-faces, and 18 8-cube 8-faces.