I am looking for an ~12x12 rectangle (small holes and small obtrusions are okay) made entirely of cube net hexominos.
It is my understanding that perfect rectangles, in general, are not possible using the set of 35 hexominos. I am aware that restricting use to only cube net polyominos exacerbates this limitation.
How close to a rectangle of order 12x12 can one get using only cube net hexominos, where the measure of distance to a 12x12 rectangle is the number of 'single-square' deletions/additions that would be necessary to delete spurious edges or and fill holes.
I would be interested in known tilings of cube net hexominos, no matter how close they are to a 12x12 rectangle.
It's possible this problem may be solvable using computer search. I'm working on that right now.