I've been doing some strange dissections lately. One is a nice puzzle -- divide a 6x6x6 cuboid into different integer-sided cuboids with volumes from 12 to 24. The solution is unique. Divide a rectangle into smaller rectangles with different sizes, but all having diagonals with the same length. The following link shows a dissection with 12 rectangles. http://math.stackexchange.com/questions/1958738/same-diagonal-dissection Use 30 or less different rectangles to bound a 3D space. No two neighboring rectangles can be in the same plane. http://community.wolfram.com/groups/-/m/t/928487 Blanche dissections, and the Mondrian puzzle http://community.wolfram.com/groups/-/m/t/903043 Zak's triangle http://community.wolfram.com/groups/-/m/t/851275 One puzzle I haven't solved -- can a cuboid be dissected into differently sized cuboids with identical volume, in a way that isn't equivalent to a 2D or stack of 2D solutions? Can different cuboids with volume 720 fill a 20x24x24 cuboid?