Polytopes Geometry Math

Polytopes

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/Sculpture and Art

• - An educational toy and industrial tool to teach geometry and model complex and simple shapes, from cubes to Fullerenes.
  
• - Enumeration, cartesian coordinates of vertices, naming, and counting the shapes.
  
• - Derivation of volume equations for regular polygons, polyhedra, and polytopes, with images.
  
• - Collection of discussions regarding volume, vertices, dissection, g-holed tori, and other subjects.
  
• - Definitions, pictures, templates, and coordinates of the regular 3d and 4d polytopes. Also includes waterman polyhedra, polar and star spheres, and the time star.
  
• - Vertex figures, filling, faceting diagrams, stellation, defining polytopes through generators, trimethoric and trisynaptic polyhedra, space-filling polyhedra, lost stellations of the icosahedron, and links.
  
• - Polytopes and optimal packing of p points in n dimensional spheres. Contains a java applet based on a model which allows for generation of multidimensional regular and semi-regular polytopes.
  
• - Comprehensive list of links to sites on geometric properties of the shapes.
  
  

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