UK Products and Services - Polyhedra and Polytopes

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A Ride Through the World of Polyhedra

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

Alexander's Polyhedra

Alex Doskey's collection of VMRL polyhedra.
(http://phobos.spaceports.com/~adoskey/polyhedra/)

Books and Articles about Polyhedra and Polytopes

Short reviews of a few of the more classic books.
(http://www.dcs.st-and.ac.uk/~ad/mathrecs/polyhedra/polyhedra)

Circumnavigating a Cube and a Tetrahedron

Discusses the shortest closed routes on the surfaces of the cube and the tetrahedron which cross or visit each face or edge, plus the shortest paths on the other three regular unit polyhedra.
(http://www.btinternet.com/~se16/js/circumnavcubetetra.htm)

Fr. Magnus Wenninger OSB

Photographs of his polyhedral constructions and links to publications.
(http://www.employees.csbsju.edu/mwenninger/)

Gallery of Polyhedra

All of the shapes can be made from books in the Tarquin catalogue. Can be viewed in virtual reality.
(http://www.tarquin-books.demon.co.uk/form/polyhedra_galler.h)

Geometric Wire Sculptures

Three-dimensional wire models available for purchase, handcrafted from stainless steel and silver soldered. They are available in several sizes.
(http://www.tacma.com/wire-sculptures/)

handsonmath.com

Geometric model building courses to improve understanding of geometry, using a Matrix kit purchasable from the site in order to create the models yourself.
(http://www.handsonmath.com/)

Jim Plank's Origami Page

Pictures and directions for creating origami polyhedra.
(http://www.cs.utk.edu/~plank/plank/pics/origami/origami.html)

Juno's World

Three dimensional block puzzles, VRML polyhedra models, instructions for creating real-world shrinkable polyhedra models, and a gallery of images. In English and Japanese.
(http://www.ne.jp/asahi/j/yananose/zindex.html)

Martin's Pretty Polyhedra

Images generated by simulating n randomly placed, mutually repelling particles on a sphere. Simulations up to n = 257.
(http://www.wmeadow.demon.co.uk/poly/)

Mathematica Graphics Gallery

A dozen polyhedral images created with Mathematica 3.0.
(http://mrc.math.hr/uvod/first_look/v30/maps/polyhedra.html)

Metal Polyhedra Models

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

Multiple-unit Dodecahedral Constructions

Images and VRML models of polyhedra connected together by their faces.
(http://home.wtal.de/mengerit/)

Netlib Repository - Polyhedra

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

Paper Models of Polyhedra

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

Pavilion of Polyhedreality

Links to polyhedra sites collected by George Hart, plus a few renderings of polyhedra.
(http://www.georgehart.com/pavilion.html)

Platonic Solids

Article in the Platonic Realms that explains why there can be only five regular polyhedra.
(http://www.mathacademy.com/pr/prime/articles/platsol/)

Platonic Spheres

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

Polygons, Polyhedra, Polytopes

An introduction to the subject of regular polytopes (generalizations of polygons and polyhedra) by Russell Towle. Includes links to related sites.
(http://home.inreach.com/rtowle/Polytopes/polytope.html)

Polyhedra by Ha Quang Le

An introduction to the basic mathematics of polyhedra, illustrated with VRML and Maple code. Details of regular polyhedra, archimedean solids, faceting, and stellating.
(http://www.scg.uwaterloo.ca/~hqle/Polyhedra/polyhedra_main.h)

Polyhedra by Jim McNeill

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

Polyhedra by Peter Cromwell

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

Polyhedra Home by Sam Gatrix

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

Polyhedra, Platonic Solids, Polytopes

Definitions, pictures, templates, and coordinates of the regular polytopes 3d and 4d.
(http://astronomy.swin.edu.au/~pbourke/polyhedra/)

polyhedra.mathmos.net

An online encyclopaedia of polyhedra and related topics, including ray-traces and other data on the Platonic Solids, Kepler-Poinsot Polyhedra, and Archimedean Solids.
(http://polyhedra.mathmos.net/)

Polyhedral Templates

Doug Zongker's templates for paper models for each of the 5 Platonic solids and the 13 Archimedean semi-regular polyhedra, in pdf format.
(http://www.cs.washington.edu/homes/dougz/polyhedra/)

Polyhedron Models Custom Built

An introduction to polyhedra by George Olshevsky, with their properties, specifications for his custom built models, and links to other pages.
(http://members.aol.com/Polycell/next.html)

Rona Gurkewitz' Modular Origami Polyhedra Page

Color photos of origami polyhedra models from Rona's origami polyhedra books.
(http://www.wcsu.ctstateu.edu/~gurkewitz/homepage.html)

Sliceform models by John Sharp

Three-dimensional objects constructed by slotting together a series of planar cross sections made from card. Downloadable templates in PDF, PS and Word formats.
(http://www.mathsyear2000.org/resources/slice/)

Stellated Icosahedra

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

Studies into Polyhedra by Anthony Thyssen

VRML polyhedra models and raw data in the OFF format to generate them, plus images of the shapes rendered with povray.
(http://www.sct.gu.edu.au/~anthony/graphics/polyhedra/)

Superliminal Software - The Geometry Page

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

Symmetry, Crystals and Polyhedra

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

The Geometry Junkyard

List of links to sites on geometric properties of polygons, polyhedra, and higher dimensional polytopes.
(http://www.ics.uci.edu/~eppstein/junkyard/polytope.html)

The Math Forum - Polyhedra

Directory of links.
(http://mathforum.org/library/topics/polyhedra/)

The Mathematical Atlas - Polytopes and Polyhedra

Collection of discussions regarding volume, vertices, dissection, g-holed tori, and others related to polytopes.
(http://www.math.niu.edu/~rusin/known-math/index/52BXX.html)

The Platonic Solids by Peter Alfeld

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.
(http://www.math.utah.edu/~alfeld/math/polyhedra/polyhedra.ht)

The Puzzling World of Polyhedral Dissections

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

The Uniform Polyhedra

Uniform polyhedra consist of regular faces and congruent vertices. Allowing for non-convex faces and vertex figures, there are 75 such polyhedra, as well as 2 infinite families of prisms and antiprisms.
(http://www.mathconsult.ch/showroom/unipoly/)

Three Puzzles with Polyhedra and Numbers

An article by Jorge Rezende, Lisbon. Includes a deltoidal icositetrahedron, rhombicuboctahedron and rhombic dodecahedron exercise. In English and Portuguese, PDF format.
(http://gfm.cii.fc.ul.pt/Members/JR.en.html)

Tom Gettys' Polyhedra Hyperpages

Ray-traced images and VRML models of platonic, archimedean, and kepler poinsot polyhedra, deltahedra, stellated polyhedra, and prisms.
(http://www.teleport.com/~tpgettys/)

Tom Lechner's Polyhedra

Images, instructions and links.
(http://www.re.org/tom/sculptures/sculptures.html)

Tom York's Polyhedron Program

Windows program, written in Borland Pascal for Windows to interactively manipulate virtual regular polyhedrons (cube, and dodecahedron) and semiregular polyhedrons (e.g. the truncated icosahedron the soccer ball shape).
(http://home.twcny.rr.com/fisheryorks/mfop/mfop.html)

Ulrich Mikloweit's Models

Graphics of paper models.
(http://www.polyedergarten.de/e_index.htm)

Un-disassemble-able Object by Jack Snoeyink

A sculpture representing research results on the number of hands that a robot would need to assemble collections of simple geometric objects.
(http://www.cs.ubc.ca/nest/imager/contributions/snoeyink/scul)

V.Bulatov's Polyhedra Collection

An extensive library of polyhedra (VRML and JPEGs).
(http://www.physics.orst.edu/~bulatov/polyhedra/index.html)

Virtual Reality Polyhedra

Encyclopedia of Polyhedra with virtual reality (VRML) models. Includes a glossary, information on the polyhedra, and a bibliography.
(http://www.georgehart.com/virtual-polyhedra/vp.html)

Waterman Polyhedra

Generated from cubic close packing lattices.
(http://www.dsuper.net/~tinom/ph2000/wp1to13.html)

Zome System in Education

Zome system is an educational toy and industrial tool to teach geometry and model complex and simple shapes from cubes to Fullerenes.
(http://www.zometool.com/edu/index.html)

Zvi Har'El

Links to a paper on uniform polyhedra and his software Kaleido for polyhedral computation and 3D display.
(http://www.math.technion.ac.il/~rl/)

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