Polytopes Geometry Math
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.
Top: Science: Math: Geometry: Polytopes
See Also:
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Numericana - Polyhedra & Polytopes - Enumeration, cartesian coordinates of vertices, naming, and counting the shapes.
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Guy's Polyhedra Pages - Vertex figures, filling, faceting diagrams, stellation, defining polytopes through generators, trimethoric and trisynaptic polyhedra, space-filling polyhedra, lost stellations of the icosahedron, and links.
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The Geometry Junkyard - Comprehensive list of links to sites on geometric properties of the shapes.
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Regular Polytopes - Derivation of volume equations for regular polygons, polyhedra, and polytopes, with images.
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The Mathematical Atlas - Polytopes and Polyhedra - Collection of discussions regarding volume, vertices, dissection, g-holed tori, and other subjects.
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The Charged Particles Model - Polytopes and optimal packing of p points in n dimensional spheres. Includes a java applet based on a model which allows for generation of multidimensional regular and semi-regular polytopes.
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Pick's Theorem - Describes a theorem for finding an area of simple lattice polygons. Includes proof and Java applet simulation.
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