Polytopes include polygons (two-dimensional), polyhedra (three-dimensional), polychora (four-dimensional), and their higher dimensional analogs. An n-dimensional polytope is built up from multiple (n-1)-dimensional polytopes. Thus, polyhedra are built up from polygons, and polychora are built up from polyhedra.
A regular polytope is composed of regular (n-1)-dimensional polytopes. There are an infinite number of regular convex polygons, five regular convex polyhedra, six regular convex polychora, and three regular convex polytopes for all dimensions five or higher.
Submit sites that discuss polytopes in general, which include regular sided geometric figures in one, two, three, four or more dimensions.
Sites about polyhedra(three dimensional) in particular should be submitted to thePolyhedra category.
Sites about regular shapes in four dimensions or more should be submitted to the Higher Dimensional category.
Higher dimensional polytopes are those of dimension four or higher. Four-dimensional polytopes in particular are called polychora.
Submit only sites that are about polytopes of the fourth or higher dimension. Sites that also cover polyhedra should go in the parent directory, Science/Math/Geometry/Polytopes/.
A polyhedron is a three-dimensional solid composed of a set of polygons connected at their edges. All of the faces of a polyhedron are flat, as opposed to spheres and cones, which have round surfaces.
Polyhedra can be regular; a regular polyhedron is one composed of regular polygons (polygons where all sides and angles are the same). There are nine regular polyhedra - five convex and five concave. The five convex polyhedra are the cube, tetrahedron, octahedron, dodecahedron, and icosahedron. These five shapes are sometimes referred to as Platonic solids.
Polyhedra composed of two different types of regular polygons are called semiregular polyhedra or Archimedean solids, of which there are thirteen.
Please submit sites that discuss the properties, graphics or history of Polyhedra. Sites which discuss Polytopes in general should be submitted to the parent category, Science/Math/Geometry/Polytopes .