Inspired by the recent thread on Hilbert curves, I decidedto think about cube filling curves that used a face diagonal as their basic move. For those of you who like to play along at home, here's an elementary formulation of the problem: Given 8 identical cubes, each marked with a line from (0,0,0) to (1,1,0), can you put them together into the [0,2]^3 cube in such a way that the marked lines form a path from (0,0,0) to (2,2,0) ? [intentional white space to hide solution] In the list below, I've identified Cubes by their vertex closest to the origin. Cube Path Start Path End ----------------------------------------- (0,0,0) (0,0,0) (1,0,1) (1,0,0) (1,0,1) (1,1,0) (0,1,0) (1,1,0) (1,2,1) (0,1,1) (1,2,1) (0,1,1) (0,0,1) (0,1,1) (1,0,1) (1,0,1) (1,0,1) (2,1,1) (1,1,1) (2,1,1) (1,2,1) (1,1,0) (1,2,1) (2,2,0) I would be interested if anyone could come up with something more pretty, either in terms of symmetry or in having fewer junction points where the path touches itself. Also, has anyone seen this space filling curve before? -Thomas C