Problems

Open Problems

There are many open problems based on the above links as well as those enumerated below.

 Polyominoes 22 holes in a one-sided pentomino construction (or a proof that this cannot be done) Maximum number of holes in a hexomino construction Multiple replications of a one-sided hexomino based on 2-2-2-2-2-2-2-4-4 or 2-2-2-2-2-2-3-3-3-3. Other constructions with the 363 octominoes without a hole. The remaining hexomino pairs in rectangles.
 Polyiamonds Further 1-3-3 constructions with the one-sided hexiamonds More multiple replications with the heptiamonds based on 2-2-4. More than 25 internal holes with the heptiamonds or a proof that 25 is the maximum. More multiple replications with the one-sided heptiamonds.
 Polyhexes 62 congruent shapes with the 620 one-sided heptahexes
 Polycubes Find a 3 x m x n box with the tetracube at the right or prove one cannot be made.
 Other Polyforms Other figures with the sliced heptiamonds Other rectangles with the thirty nine perimeter 9 polyares