Search for developments of a box having multiple ways of folding by SAT solver
This work addresses a combinatorial geometry problem for researchers in mathematics and computer science, but it is incremental as it builds on known concepts using computational methods.
The researchers tackled the problem of finding polyominoes that can fold into a box in multiple ways by conducting a computer search using a SAT solver, resulting in the discovery of thousands of such developments, including one with area 52 that folds into a 1x2x8 box in five different ways.
A polyomino is called a development if it can make a box by folding edges of unit squares forming the polyomino. It is known that there are developments that can fold into a box (or boxes) in multiple ways. In this work, we conducted a computer search for finding such developments by using a SAT solver. As a result, we found thousands of such developments including a polyomino of area 52 that can fold into a box of size $1 \times 2 \times 8$ in five different ways.