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It is extremely difficult. In fact the 15 class of pentagon was only discovered in 2015.
All triangles will tessellate. All quadrilaterals will tessellate 15 classes of irregular convex pentagons will tessellate. Regular hexagons will tessellate as will 3 classes of irregular convex hexagons which will tessellate. No convex polygon with 7 or more sides will tessellate.


Then, there are concave polygons as well as non-polygonal shapes which will tessellate. One interesting collection of examples is MC Escher's set of symmetric artwork from 1942, mostly watercolours.

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9y ago

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