polyhedra

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Transformation of the Plane

Xah Lee , 1996-08, 2008-02 What follows are images of Transformation of the Plane. The original image is a square grid. The transformed image is shown, under a function f.

http://xahlee.org/MathGraphicsGallery_dir/Transform2DPlot_dir/transform2DPlot.html

It's important to have the Java "Just In Time Compiler" enabled on your browser because this applet needs all the speed it can get. If you didn't specifically disable the JIT compiler in your browser settings, it's probably enabled. See my Stellations of the Dodecahedron applet to see how a "Star Polyhedron" is generated in 3 dimensions.

http://dogfeathers.com/java/hyperstar.html

Hyperspace Star Polytope Slicer

Pavilion of Polyhedreality

http://web.archive.org/web/20070203230240/www.georgehart.com/pavilion.html

Note: For your maximal synesthetic enjoyment, I have chosen short musical selections to go with each picture. If your web viewer is set up to play MIDI music files , just click on any of the red notes before selecting a picture, and you can listen to a J.S. Bach piece as background music while each image is transferring. The following images are available at the moment:

Uniform polyhedra - polyhedra with regular (not necessary convex) faces and symmetrically equivalent vertices. Duals to uniform polyhedra. Compounds of uniform and dual polyhedra. Johnson's solids - all convex nonuniform polyhedra with regular convex faces. 59 stellations of icosahedron.

V.Bulatov's Polyhedra Collection

http://web.archive.org/web/20060718050434/www.physics.orst.edu/~bulatov/polyhedra/index.html

http://web.archive.org/web/20070207101515/members.aol.com/Polycell/next.html

Just added November 22, 2004: A website where you can view and even purchase beautiful prints of interesting polychora nets. Go to Nuts About Nets! Above: Painting of Fra Luca Pacioli and pupil, by Jacopo de Barbari (1440/50?–1516), perhaps the most famous Renaissance painting with a geometric theme. Currently at the Museo di Capodimonte in Naples, Italy, it was executed in 1495, and besides the figures of Renaissance geometer Pacioli and an unnamed mathematics student, it shows a beautiful glass model rhombicuboctahedron suspended by a string and a paper or wooden model regular dodecahedron on the bench. YMMETRIC FIGURES in solid geometry have fascinated people since ancient times.

Polycell's Home Page

Set Nr. 6. Father Magnus Wenninger OSB. Polyhedron Models for th

Select a thumbnail to see a larger version. Many of the models below were included in an exhibition at the College of Saint Benedict , St. Joseph, MN. The models with a green background were photographed in September 2006.

http://www.saintjohnsabbey.org/wenninger/2002.html

e_info

The sequence and the combination of the models on the sites are not systematical.The names and the w-numbers (for example w85: Quasirhombicuboctahedron) are taken from M. Wenningers book "Polyhedron models" . Sort and number of the faces of most of the models are given. On the following sites and the links there you find nearly everything which is known about polyhedra.There are thousands of wonderful images, animated ones and models that can be moved with the mouse:

Platonic | Archimedean/Catalan | Kepler-Poinsot | Prisms/Antiprisms | Uniform/Dual | Stellations | Miscellaneous | Tips This page contains images of polyhedra I have made using nets created by the program Stella4D , Great Stella or Small Stella . Click on one of the links below to see all the models in that category. If you want to see some of my older models, which were made without the aid of a computer, see here .

Rob's Polyhedron Models

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