The inherent computational complexity of polygon decomposition problems is of importance in the field of computational geometry. For one of these problems it is shown that the three-dimensional version is NP-complete whereas its two-dimensional version is polynomial. This provides an example for the conjecture posed by O'Rourke and Supowit.
Dielissen, V. J., & Kaldewaij, A. (1991). Rectangular partition is polynomial in two dimensions but NP-complete in three. Information Processing Letters, 38(1), 1-6. https://doi.org/10.1016/0020-0190(91)90207-X