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Stick puzzles use sets of 'polysticks' (essentially one-dimensional objects) which have to be assembled into two- or three-dimensional configurations.
Polysticks are configurations of joined or unjoined thin (ideally one-dimensional) 'sticks'. The sticks may be matchsticks, or pieces of straw, wire or similar.
A special (and very old) class of stick puzzles are 'matchstick puzzles', where all parts used are sticks (usually matchsticks) rather than polysticks. Some (trick-)puzzles can only be solved when one assumes that the sticks actually have measurements in more than one dimension.