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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.
http://www.numericana.com/answer/polyhedra.htm
Enumeration, cartesian coordinates of vertices, naming, and counting the shapes.
http://www.cut-the-knot.org/ctk/Pick.shtml
Describes a theorem for finding an area of simple lattice polygons. Includes proof and Java applet simulation.
http://www.ics.uci.edu/~eppstein/junkyard/polytope.html
Comprehensive list of links to sites on geometric properties of the shapes.
http://www.zometool.com/
Educational toys used to teach geometry and model building to create squares, spheres, stars and other regular shapes with sticks and connecting pieces.
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