Directory of Polyhedra Resources

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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 can be regular; a regular polyhedron is one composed of regular polygons (polygons where all sides and angles are the same). There are nine regular polyhedra - five convex and five concave. The five convex polyhedra are the cube, tetrahedron, octahedron, dodecahedron, and icosahedron. These five shapes are sometimes referred to as Platonic solids. Polyhedra composed of two different types of regular polygons are called semiregular polyhedra or Archimedean solids, of which there are thirteen.

Resources in This Category

• A Ride Through the Polyhedra World

  http://www.ac-noumea.nc/maths/polyhedr/index_.htm
  Provides animations and video clips of convex polyhedra, non convex polyhedra, other polyhedra and related subjects. In French and English.

• Handsonmath.com

  http://www.handsonmath.com/
  Abstract of book about geometric model building.

• Harold Scott MacDonald Coxeter

  http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Coxeter.html
  Biography from an online History of Mathematics, with quotes.

• Juno's World

  http://www.polyhedra.jp/
  Three dimensional block puzzles, VRML models, instructions for creating real-world shrinkable models, and a gallery of images. In English and Japanese.

• Mathematician's Portrait - Professor Emeritus H.S.M. Coxeter

  http://www.math.toronto.edu/~coxeter/
  Short biography from the University of Toronto.

• Metal Polyhedra Models

  http://www.peda.com/models/
  A set of eight solid aluminum models for purchase, available in several colors.

• Multiple-unit Dodecahedral Constructions

  http://home.wtal.de/mengerit/
  Images and VRML models of the shapes connected together by their faces.

• Netlib Repository - Polyhedra

  http://www.netlib.org/polyhedra/
  Data files and sample C code for a large number of the shapes.

• Paper Models of Polyhedra

  http://www.korthalsaltes.com/
  More than eighty paper model templates, ready to cut out and fold up, available to print out or download.

• Pavilion of Polyhedreality

  http://www.georgehart.com/pavilion.html
  List of links to sites on the topic, plus a few renderings of the shapes.

• Platonic Solids

  http://www.mathacademy.com/pr/prime/articles/platsol/
  Explains why there can be only five regular polyhedra.

• Platonic Spheres

  http://www.neubert.net/PLASpher.html
  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.

• Polyedergarten

  http://www.polyedergarten.de/e_index.htm
  Images of paper models, plus some vrml models. In English, German, and French.

• Polyhedra Home by Sam Gatrix

  http://gratrix.net/polyhedra/
  Hundreds of ray-traced polyhedra, their duals, and their properties, plus Polyhedra 2001, a real-time viewer available for download (uses OpenGL).

• polyhedra.mathmos.net

  http://polyhedra.mathmos.net/
  An online encyclopedia of the shapes, including ray-traces and other data on the Platonic Solids, Kepler-Poinsot Polyhedra, and Archimedean Solids.

• Stellated Icosahedra

  http://www.mathconsult.ch/showroom/icosahedra/
  Background information and images of the 59 possible stellated icosahedra.

• Superliminal Software - The Geometry Page

  http://www.superliminal.com/geometry/geometry.htm
  Discussion of deltahedra, infinite and flexible polyhedra, with images, a java applet, and links.

• Symmetry, Crystals and Polyhedra

  http://www.uwgb.edu/dutchs/symmetry/symmetry.htm
  Data on polyhedra, the different types, compounds of the shapes, stellations, stewart toroids, zonohedra, and tesselations. Also discusses crystallography and symmetry.

• The Platonic Solids by Peter Alfeld

  http://www.math.utah.edu/~alfeld/math/polyhedra/polyhedra.html
  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.

• The Puzzling World of Polyhedral Dissections

  http://www.johnrausch.com/PuzzlingWorld/contents.htm
  Puzzle designer's guidebook with designs, plans, and instructions for building geometric dissection puzzles of polyhedra and burrs.

• The Uniform Polyhedra

  http://www.mathconsult.ch/showroom/unipoly/
  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.

• Three Puzzles with Polyhedra and Numbers

  http://gfm.cii.fc.ul.pt/people/jrezende/jr_poliedros-puzzles_en.pdf
  An article by Jorge Rezende, Lisbon. Includes a deltoidal icositetrahedron, rhombicuboctahedron and rhombic dodecahedron exercise.

• Virtual Reality Polyhedra

  http://www.georgehart.com/virtual-polyhedra/vp.html
  Encyclopedia with virtual reality (VRML) models, history and art of the shapes. Includes background information on each shape, a glossary, guide to names, classroom activities, sculptures by the author, and a bibliography.

• Vladimir Bulatov Polyhedra Collection

  http://bulatov.org/polyhedra/
  Collection of information on polyhedra with images, VRML files, interactive java applets and original research.

• Zvi Har'El

  http://www.math.technion.ac.il/~rl/
  Features a paper on uniform polyhedra and Kaleido software for computation and display of the shapes.

Related Categories

• Home > Science > Math > Geometry > Solid Geometry

 

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