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.

## Cross-polytope

In geometry, a cross-polytope, orthoplex, hyperoctahedron, or cocube is a regular, convex polytope that exists in n-dimensions.

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## E9 honeycomb

In geometry, an E9 honeycomb is a tessellation of uniform polytopes in hyperbolic 9-dimensional space.

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## Gosset–Elte figures

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.

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## Hexadecagon

In mathematics, a hexadecagon (sometimes called a hexakaidecagon) or 16-gon is a sixteen-sided polygon.

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## List of mathematical shapes

Following is a list of some mathematically well-defined shapes.

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## List of polygons, polyhedra and polytopes

A polytope is a geometric object with flat sides, which exists in any general number of dimensions.

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## List of regular polytopes and compounds

This page lists the regular polytopes and regular polytope compounds in Euclidean, spherical and hyperbolic spaces.

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## Nine-dimensional space

In mathematics, a sequence of n real numbers can be understood as a point in n-dimensional space.

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## Octadecagon

An octadecagon (or octakaidecagon) or 18-gon is an eighteen-sided polygon.

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## Polytope families

There are several families of symmetric polytopes with irreducible symmetry which have a member in more than one dimensionality.

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## Rectified 9-cubes

In nine-dimensional geometry, a rectified 9-cube is a convex uniform 9-polytope, being a rectification of the regular 9-cube.

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## Rectified 9-orthoplexes

In nine-dimensional geometry, a rectified 9-simplex is a convex uniform 9-polytope, being a rectification of the regular 9-orthoplex.

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## Uniform 9-polytope

In nine-dimensional geometry, a nine-dimensional polytope or 9-polytope is a polytope contained by 8-polytope facets.

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## Uniform k 21 polytope

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.

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## 10-orthoplex

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.

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## 8-simplex

In geometry, an 8-simplex is a self-dual regular 8-polytope.

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## 9-cube

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.

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## Redirects here:

6 11 polytope, 9-cross, 9-cross polytope, 9-cross-polytope, Enneacross, Pentacosidodecayotton.