An old problem in combinatorial geometry is to find the smallest
solid box that a polycube can tile.
See, for example, Pentacubes in a Box.
Here I show minimal results for a broader problem:
find the smallest prism that a polycube can tile.
Some polycubes that cannot tile boxes can tile prisms.
I do not show flat polycubes, which are prisms in their own right.
Sometimes we can use fewer tiles by letting the hexacube be reflected:
Last revised 2017-10-22.
Back to Polyform Tiling
Col. George Sicherman