9 23 11 TESSELLATIONS Tessellation Tiling a plane Filling a plane with a shape or image no gaps From Latin tessella a small cubical piece of clay stone or glass used to make mosaics The word tessella means small square from tessera square which in its turn is from the Greek word for four Wikipedia 1 9 23 11 Regular Tessellations Only three regular tilings all the same shape Variations on these regular shapes work too Semi Regular Tessellations Two or more regular polygons 8 possibilities 2 9 23 11 Demiregular Tessellations Harder to define Tile a plane with images Escher 3 9 23 11 M C Escher Dutch graphic artist 1898 1972 known for his often mathematically inspired woodcuts lithographs and mezzotints These feature impossible constructions explorations of infinity architecture and tessellations Wikipedia Tile a plane with images Escher 4 9 23 11 Tile a plane with images Escher VLSI Version 5 9 23 11 How to do it Exploit symmetries Translation Rotation Reflection Start with a regular tessellation square triangle hexagon Then apply transformations and see what they end up looking like Simple example Translation Start with a square http euler slu edu escher index php Tessellations by Recognizable Figures 6 9 23 11 Simple example Translation Start with a square in this example It works for any of the regular tessellations The Tessellation Project Simple example Glide Reflection Start with a triangle The Tessellation Project 7 9 23 11 Simple example Reflection Start with a triangle Tessellations org Simple example Reflection Start with a triangle Tessellations org 8 9 23 11 Escher Translation Translation http euler slu edu escher index php Tessellations by Recognizable Figures 9 9 23 11 Other Symmetries Translation Rotation Reflection Using squares triangles and hexagons http www dustinjpurdy com Math PDF Tessellation pdf The Nine Heesch Types Tessellation classification code developed by German mathematician Heinrich Heesch http www dustinjpurdy com Math PDF Tessellation pdf 10 9 23 11 For your Tesselations Start with a regular tessellation grid vertices only can be a good way to go too Then start tweaking the lines according to the transformations and see what it looks like Some Web Sources good info http euler slu edu escher index php Tessellations by Recognizable Figures http www dustinjpurdy com Math PDF Tessellation pdf http library thinkquest org 16661 http tessellations org http www mcescher com 11 9 23 11 One more Escher Reptiles 12
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