Other Online Resources on 4D
The Higher Dimensions Forum, and its associated wiki. Originally inherited from Garrett Jones' now-defunct tetraspace page, it has grown over the years into an excellent source of information on the subject of higher-dimensional spaces and speculation related to universes with more than 3 spatial dimensions.
Edwin A. Abbott's Flatland: A romance of many dimensions. A novel that gives wonderful insight into dimensional analogy.
And He Built a Crooked Houseby Robert A. Heinlein. An entertaining story about a house in the shape of a hypercube.
Dr. Richard Klitzing's polytopes and incidence matrices. Contains a wealth of technical details about higher-dimensional polytopes (not limited to 4D) and related geometric concepts, including exhaustive information on a large number of polytopes.
Uniform Polytopes in Four Dimensions, by George Olshevsky. This site has an immense catalogue of uniform 4D polytopes and their various properties.
Uniform Polychora by Jonathan Bowers, who discovered a very large number of uniform 4D polytopes (most of which are non-convex).
The Fourth Dimension. After the initial introduction to 4D, this page gives a very good explanation of how the 120-cell is constructed.
Games & Tools:
4D Blocks by John McIntosh: an enhanced version of the original 4D maze, this amazing game takes you to an actual 4D world in first-person perspective, and lets you pick up 4D objects and move them around. Comes with a very large set of premade scenes and objects that you can play with, and even sports a train that moves around train tracks in real-time! A very highly recommended way of exploring a truly 4D world.
4D building blocks! Written by Henryk Trappmann. A really awesome way of learning 4D, by assembling 4D blocks together. If you can solve all 6 scenarios in the game, you'd have a pretty good grasp on 4D geometry.
Magic Cube 4D: play with a 4D Rubik's Cube! (As if the 3D one isn't hard enough already!) If you can master this game, you will have a very good grasp on 4D rotations.
Magic 120-cell: as if the 4D Rubik's Cube isn't enough, this one is the 4D analogue of the Megaminx puzzle. This puzzle has 120 cells, each of which is a dodecahedron divided into 63 movable pieces, for a whopping total of 2641 pieces with 7560 colored hyper-stickers. If you think you know 4D, prove it by solving this one!
Already mastered 4D? Craving for a challenge? Try Magic Cube 5D. See if you can get into the Hall of Insanity!
Still not satisfied? 5D not enough for you? For a real challenge, try Magic Cube 7D. Guaranteed to blow your puny little mind into 78110 pieces!
Nklein software's multi-dimensional ray-tracer. This one lets you do not just 4D ray-tracing, but ray-tracing in any number of dimensions.
Papers and other technical resources:
Steve Hollasch's M.Sc. thesis on 4D ray-tracing. A very good overview of the issues involved in visualizing 4D space.
Geometry for N-Dimensional Graphics [PDF] by Andrew J. Hanson. Good description of geometric formulas for an arbitrary number of dimensions.
The Polygloss, Wendy Krieger's glossary of higher-dimensional terms designed to avoid the confusion caused by the inconsistent application and generalization of our 3D-centric terminology to higher dimensions. This is the place to go if you want very precise terminology for describing various aspects of higher-dimensional spaces.