Four-dimensional Euclidean space is very fascinating. It has “room” to do all sorts of interesting things you can’t do in cramped, provincial 3-D, yet it is not as boringly “loose” as Euclidean spaces of five and more dimensions.

Of course, it’s hard (not, on the testimony of the late H.S.M. Coxeter, the 20th century’s greatest geometer, impossible, but hard) to visualize 4-D objects. You can, though, slice ‘em up with 3-dimensional hyper-cleavers, then examine the sections. Here is the kind of thing you get. Note: If you have a pair of 3-D red-green glasses, it’s even more fun. If you have a pair of 4-D glasses, of course, you don’t really need the website…

(Thanks to Charles Martin for this.)