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Polyhedra

Science > Math > Geometry > Polytopes > Polyhedra

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A Ride Through the World of Polyhedra - http://www.ac-noumea.nc/maths/amc/polyhedr/index_e.htm
Images, properties, constructions, and java applets to rotate the shapes. Includes convex, non-convex, and other polyhedra, plus links to other sites.

Alexander's Polyhedra - http://phobos.spaceports.com/~adoskey/polyhedra/
Alex Doskey's collection of VMRL models. Includes a concentric model of the five platonic solids, Stewart G3's, toroidal polyhedra, and other shapes.

Circumnavigating a Cube and a Tetrahedron - http://www.btinternet.com/~se16/js/circumnavcubetetra.htm
Discusses the shortest closed routes which cross or visit each face or edge on the surfaces of the five regular polyhedra.

Gallery of Polyhedra - http://www.tarquin-books.demon.co.uk/form/polyhedra_galler.html
Gallery of shapes that can be made from books in the Tarquin catalogue, with some VRML models.

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.

Martin's Pretty Polyhedra - http://www.wmeadow.demon.co.uk/poly/
Images generated by simulating n randomly placed, mutually repelling particles on a sphere. Simulations up to n = 257.

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 by Jim McNeill - http://web.ukonline.co.uk/polyhedra/
Collection of VRML models generated by a QuickBasic program named Hedron. A number of the models aren't seen elsewhere.

Polyhedra by Peter Cromwell - http://www.liv.ac.uk/~spmr02/book/
Contents, reviews, and errata of the book (CUP, 1997).

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 Models by Doug Zongker - http://www.isotropic.org/uw/polyhedra/
Templates for paper models for each of the 5 Platonic solids and the 13 Archimedean semi-regular polyhedra, in pdf format.

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.

Studies into Polyhedra by Anthony Thyssen - http://www.sct.gu.edu.au/~anthony/graphics/polyhedra/
VRML models and raw data in the OFF format to generate the shapes, plus images of the shapes rendered with povray.

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.

Tom Gettys' Polyhedra Hyperpages - http://home.comcast.net/~tpgettys/
Ray-traced images and VRML models of platonic, archimedean, and kepler poinsot polyhedra, deltahedra, stellated polyhedra, and prisms.

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.

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