3D Polyhedra
This is a polyhedra megapage with a lot of links about Polyhedra. There are links to polyhedra of the third dimension and polychora of the fourth dimension, which are analogues of polyhedra. There are links to regular polychora (called polytopes) and a link to a polytope viewer which can show 3d cross sections of polytopes having four or more dimensions. There are also pages on general geometry, which includes links on 3rd and 4th dimension geometry) and just for fun, there are links with info on how polyhedra relate to crystal structure, and the shape of fair dice. Be sure to look at the Pick polytope viewer and check out the dice! One can look at the geometry links to find more about geometry. Don't forget to view the special kind of polyhedras by clicking on each picture! (The Deltahedra page, which show solids made up of only equilateral triangles, may make one be overawed by the shapes that can exist with only triangles.
Download a virtual reality player and check out the virtual reality polyhedra designed by George Hart.
Gijs Korthals Altes has a wonderful page on polyhedra which show paper models with instructions with how to construct them. This page also has caleidocycli, which are rings (made only of tetrahedrons) which can be turned inside out. Check out the Caledocycli pages for come details on construction. There also some links on Plato, and Archimedies, the discoverer of many polyhedra, paper model links, and links on miscellaneous models on the bottom of the page. This is quite a "hands on" way to study polyhedra.
Philosophy of Science's Polyhedra Page has a descpiption of what polyhedra and polytopes are all about, as well as tables which show the number of edges, faces, vertices, the type of polygon, and the number of polyhedra (solids or in this case "cells) for polytopes. This is a chart showing relations between polyhedra and polytopes. It may be bland compared to other pages. but it may help in geometry homework.
Steffen Weber has posted Java applets that let you see all kinds of polyhedra rotating in space.
Polytopes
Visit the polytope page of the Geometry Junkyard. There are too many links to follow from here!
Here is Micheal Gibbs' 4-D Polytope Viewer java applet, which shows various wire frame models of four dimensional polytopes, including a hyperdubical grid, which is the counterpart to the square and cubical grids. There some instructions on how to view the images as well as some inferesting properties of the 4D objects. One can also download programs to view polytopes from the same page. The links to these programs are near the bottom of the page. This also provides a way to take a peek into the fourth dimension. (no pun intended)
Here is an interesting discussion about the four dimensional analogs of the Platonic solids, which fall in the class of polytopes. This page by Dr. Jodi called "Ask Dr. Math," also has interesting links for further exploration.
Superliminal Software has its own geometry page, which contain some links and interesting info on infinite polyhedra (yes, they really do exist!) deltahedra (mentioned before) and flexible polyhedra. (I never knew polyhedra can bend!) This page also has links to interactive 3D models of polyhedra of the flexible or infinite kind. There are more to plolyhedra than just only the Archimedian and Platonic kind. See the strange new world of flexible and infinite polyhedra!
Fourth Dimension
4D Nexus is a page with info on the 3rd and 4th dimensions, and space and time. It has links to topics, pages with pictures and videos, and 4D inspired artwork, and pages to books about the fourth dimension. The 3D section has only links to products, while links to general information about the third dimension is on another page. This is an okay site for looking for links for topics on the third and fourth dimension, but currently it is sparse on links. The page will have its official release on the first day of March 2000, so hope there will be more links by then.
And don't forget to read the online text of Edwin Abbott Abbott's Flatland. This link is a little better than the one from the homework page, because it has illustrations and better navigation.