Multidimensional Crosswords?

Aaron asks: "I write the crossword for the student newspaper at my university (McGill, in Montreal). For the last issue of the year I like to go all-out and do something special. Usually I just make a super-big one, but I had a brainstorm - a crossword is essentially a 2-dimensional matrix where set intersections are judged as valid if they test positive as real words out of a dictionary. Of course, the decision to limit the matrix to 2 dimensions is just pragmatic so if you wanted you could make crosswords of 3 or more dimensions (though a 4-dimension crossword might have to be done in pencil first). Any ideas on how to actually do this?" This would be interesting on a computer, but would be fairly hard to do in print. If you were of a mind to make a 3D crossword puzzle on paper, how would you do it?