Polyhedra Polytopes Geometry

Polyhedra

A polyhedron is a three-dimensional solid composed of a set of polygons connected at their edges. All of the faces of a polyhedron are flat, as opposed to spheres and cones, which have round surfaces. Polyhedra composed of two different types of regular polygons are called semiregular polyhedra or Archimedean solids, of which there are thirteen.

• Top/Science/Math/Geometry/Solid Geometry

• - Images, properties, constructions, and java applets to rotate the shapes. Includes convex, non-convex, and other polyhedra, plus links to other sites.
  
• - Data on polyhedra, the different types, compounds of the shapes, stellations, stewart toroids, zonohedra, and tesselations. Also discusses crystallography and symmetry.
  
• - Excerpt of Chapter 9 of R. Maeder's book The Mathematica Programmer II. Includes images and statistics for 80 uniform polyhedra, plus background information on the shapes and the wythoff symbol.
  
• - An introduction to the shapes by George Olshevsky, with their properties, specifications for his custom built models, and links to other pages.
  
• - Images of paper models, plus some vrml models. In English, German, and French.
  
• - Three dimensional block puzzles, VRML models, instructions for creating real-world shrinkable models, and a gallery of images. In English and Japanese.
  
• - Convex hulls generated from the mathematics of cubic close packing using a radial sweep algorithm, up to the square root of 94.
  
• - VRML models and raw data in the OFF format to generate the shapes, plus images of the shapes rendered with povray.
  
• - Contents, reviews, and errata of the book (CUP, 1997).
  
• - System that can take 3d structure descriptions and generate mouse-rotatable flash animations out of them. Examples of animations for the five regular polytopes. In Chinese and English.
  
• - Collection of VRML models generated by a QuickBasic program named Hedron. A number of the models aren't seen elsewhere.
  
• - Photographs of his constructions and a bibliography of works by and about him.
  
• - An online encyclopedia of the shapes, including ray-traces and other data on the Platonic Solids, Kepler-Poinsot Polyhedra, and Archimedean Solids.
  
• - An extensive library of images and vrml models of the shapes. Includes uniform polyhedra, stellations, spherical platonic polyhedra, polyhedral mirrors, hyperbolic tesselations, plates from Bruckner's 1906 polyhedra book, and a stellation java applet.
  
• - Alex Doskey's collection of VMRL models. Includes a concentric model of the five platonic solids, Stewart G3's, toroidal polyhedra, and other shapes.
  
• - Biography from an online History of Mathematics, with quotes.
  
• - A set of eight solid aluminum models for purchase, available in several colors.
  
• - Ray-traced images and VRML models of platonic, archimedean, and kepler poinsot polyhedra, deltahedra, stellated polyhedra, and prisms.
  
• - Gallery of shapes that can be made from books in the Tarquin catalogue, with some VRML models.
  
• - List of links to sites on the topic, plus a few renderings of the shapes.
  
• - A dozen images of stellations and truncations created with Mathematica 3.0.
  
• - More than eighty paper model templates, ready to cut out and fold up, available to print out or download.
  
• - Hundreds of ray-traced polyhedra, their duals, and their properties, plus Polyhedra 2001, a real-time viewer available for download (uses OpenGL).
  
• - Images and VRML models of the shapes connected together by their faces.
  
• - Features a paper on uniform polyhedra and Kaleido software for computation and display of the shapes.
  
• - Short biography from the University of Toronto.
  
• - Geometric model building courses to improve understanding of geometry, using a Matrix kit for sale on the site that can be used in order to create the models yourself.
  
• - Templates for paper models for each of the 5 Platonic solids and the 13 Archimedean semi-regular polyhedra, in pdf format.
  
• - Discussion of deltahedra, infinite and flexible polyhedra, with images, a java applet, and links.
  
• - Data files and sample C code for a large number of the shapes.
  
• - Discusses the shortest closed routes which cross or visit each face or edge on the surfaces of the five regular polyhedra.
  
• - Puzzle designer's guidebook with designs, plans, and instructions for building geometric dissection puzzles of polyhedra and burrs.
  
• - The five regular polyhedra mapped onto the surface of their surrounding spheres, which can be rotated in java applets. Also includes a discussion of the mathematical properties of the shapes.
  
• - An article by Jorge Rezende, Lisbon. Includes a deltoidal icositetrahedron, rhombicuboctahedron and rhombic dodecahedron exercise. In English and Portuguese, PDF format.
  
• - Background information and images of the 59 possible stellated icosahedra.
  
• - Explains why there can be only five regular polyhedra.
  
• - Images and equations for regular polyhedra, plus some links.
  
• - Images generated by simulating n randomly placed, mutually repelling particles on a sphere. Simulations up to n = 257.
  
• - A proof that each configuration of polygons around a vertex results in a unique polyhedron, plus Java applets for rotating the images of the shapes.
  
  

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