Geometry on the Web

There are many excellent (and many not so excellent) web sites on geometric topics such as polyhedra, tilings and symmetry; many of these sites contain outstanding graphics, and extensive lists of links. Here are a few nice sites that I have come across, though searching the web will most likely lead you to many other worthwhile sites.

Geometry in General

• Geometry Junkyard http://www.ics.uci.edu/~eppstein/junkyard/

A very nice site covering all sorts of geometric topics, with many excellent links. A very good place to start searching for specific topics.

• Geometry in Action http://www.ics.uci.edu/~eppstein/geom.html

By the same person who does "Geometry Junkyard," this set of links focuses on real world applications of geometry.

• Geometry Center http://www.scienceu.com/geometry/

The Geometry Center is a mathematical research institute that, in addition to promoting research, wants to reach out to a broader public.

Symmetry

• Symmetry and the Shape of Space http://comp.uark.edu/~cgstraus/symmetry.unit/index.html
• Tour of Symmetry Groups http://www.geom.umn.edu/~lori/kali/
• Dror Bar-Natan's Symmetry Page http://www.math.toronto.edu/~drorbn/Gallery/Symmetry/index.html
• Examples of Symmetry Groups http://www.spsu.edu/math/tile/symm/types/index.htm
• Historical Examples of Symmetry Groups http://www.spsu.edu/math/tile/grammar/index.htm
• More Examples of Symmetry Groups http://www.tessellations.org/index.htm
• Alhambra http://www.pbase.com/abwhitt/alhambra_granada
• More Alhambra http://homepages.tcp.co.uk/~nicholson/alhambra.html
• Yet More Alhambra http://home.earthlink.net/~mayathelma/sitebuildercontent/sitebuilderfiles/alhambra.tlc.2004.pdf
• Escher http://www.mathacademy.com/pr/minitext/escher/

Polygons and Tilings

• Totally Tessellated http://library.advanced.org/16661/

A very nice site, with thorough discussion of tesselations using nice graphics and animation. A bit tricky to find one's way around -- using the site map helps. Nice collection of links.

Polyhedra

• Virtual Reality Polyhedra http://www.georgehart.com/virtual-polyhedra/vp.html

This site has a very thorough discussion of various types of polyhedra, as well as outstanding graphics. To view the graphics you need special software, which can be downloaded for free, as explained at this site.

• Symmetry, Crystals and Polyhedra http://www.uwgb.edu/dutchs/symmetry/symmetry.htm

This site has some very good pictures of various categories of polyhedra.

• MathWorld by Eric W. Weisstein -- Polyhedra http://mathworld.wolfram.com/Polyhedron.html

Extensive discussion of polyhedra.

Higher Dimensions

• Flatland http://www.geom.umn.edu/~banchoff/Flatland/

This site has the complete text (with illustrations) of "Flatland," the classic tale of a creature from a two-dimensional world who encounters higher dimensions.

• Peek http://www.graphics.cornell.edu/~gordon/peek/peek.html

Peek is a program that interactively explores higher dimensional polytopes through the use of cross-sections and projections, which give us an additional way to gain geometric insight into higher dimensions.