Problems
Open Problems
There are many open problems based on the above links as well as those enumerated below.
Polyhexes 
62 congruent shapes with the 620 onesided 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 