# Directory of Polytopes Resources

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.

## Resources in This Category

• #### Numericana - Polyhedra & Polytopes

Enumeration, cartesian coordinates of vertices, naming, and counting the shapes.

• #### Pick's Theorem

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.

• #### The Geometry Junkyard

http://www.ics.uci.edu/~eppstein/junkyard/polytope.html
Comprehensive list of links to sites on geometric properties of the shapes.

• #### Zometool

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.

## Related Categories

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