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Given a chain of HW cubes where each cube is marked "turn 90^" or "go straight", when can it fold into a 1 H W rectangular box? We prove several variants of this (still) open problem NP-hard: (1) allowing some cubes to be wildcard (can turn or go straight) ; (2) allowing a larger box with empty spaces (simplifying a proof from CCCG 2022) ; (3) growing the box (and the number of cubes) to 2 H W (improving a prior 3D result from height 8 to 2) ; (4) with hexagonal prisms rather than cubes, each specified as going straight, turning 60^, or turning 120^; and (5) allowing the cubes to be encoded implicitly to compress exponentially large repetitions.
Group et al. (Sun,) studied this question.