Edge Tessellations and Stamp Folding Puzzles

• Autores: Matthew Kirby, Ronald N. Umble
• Localización: Mathematics magazine, ISSN 0025-570X, Vol. 84, Nº. 4, 2011, págs. 283-289
• Idioma: inglés
• DOI: 10.4169/math.mag.84.4.283
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• Resumen

  • An edge tessellation is a tiling of the plane generated by reflecting a polygon in its edges. In this article we prove that a polygon generating an edge tessellation is one the following eight types: a rectangle; an equilateral, 60-right, isosceles right, or 120-isosceles triangle; a 120-rhombus; a 60-90-120 kite; or a regular hexagon. A stamp folding puzzle is a paper folding problem constrained to the perforations on a sheet of postage stamps. Such sheets necessarily embed in an edge tessellation. On page 143 of his book Piano-Hinged Dissections: Time to Fold!, G. Frederickson poses the following conjecture: �Although triangular stamps have come in a variety of different triangular shapes, only three shapes seem suitable for [stamp] folding puzzles: equilateral, isosceles right triangles, and 60º-right triangles.� We prove that the four non-obtuse polygons mentioned above generate edge tessellations suitable for stamp folding puzzles. Our proof of suitability, which establishes Frederickson�s Conjecture, exhibits explicit algorithms for folding each suitable edge tessellation into a packet of single stamps.