Directory of Polytopes Resources

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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.

Subcategories

• Higher Dimensional
• Origami Polyhedra
• Polyhedra
• Software

Resources in This Category

• Numericana - Polyhedra & Polytopes

  http://www.numericana.com/answer/polyhedra.htm
  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

• Home > Science > Math > Geometry > Sculpture and Art
• Home > Science > Math > Recreations > Tessellations

 

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