Polyhedra Polytopes Geometry

@Intermall

Top: Science: Math: Geometry: Polytopes: Polyhedra:

• Top/Science/Math/Geometry/Solid Geometry

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