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  3. Schwarz triangle - Wikipedia

    en.wikipedia.org/wiki/Schwarz_triangle

    This process can be repeated for P 2 to get P 3 by first adding tiles to each edge of P 2 and then filling in the tiles round each vertex of P 2. Then the process can be repeated from P 3, to get P 4 and so on, successively producing P n from P n – 1. It can be checked inductively that these are all convex polygons, with non-overlapping tiles.

  4. Packing problems - Wikipedia

    en.wikipedia.org/wiki/Packing_problems

    The study of polyomino tilings largely concerns two classes of problems: to tile a rectangle with congruent tiles, and to pack one of each n-omino into a rectangle. A classic puzzle of the second kind is to arrange all twelve pentominoes into rectangles sized 3×20, 4×15, 5×12 or 6×10.

  5. Mathematics of paper folding - Wikipedia

    en.wikipedia.org/wiki/Mathematics_of_paper_folding

    Two-colorability Angles around a vertex. The construction of origami models is sometimes shown as crease patterns. The major question about such crease patterns is whether a given crease pattern can be folded to a flat model, and if so, how to fold them; this is an NP-complete problem. [32]

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