In the pallet loading problem, we are asked to place a set of small identical 2-D rigid objects into a large bounding rectangle such that no two objects overlap. This problem is a special case of the cutting stock problem and is known to be NP-complete. It is NP-complete even for the special case in which the objects are identical squares [Fowler, Paterson, Tanimoto 1981].
Is pallet loading also NP-complete when the objects are non-rectangular? In particular, I am interested the case in which the objects are octagons.