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A Tessellation is a pattern of regular shapes that completely covers a plane surface. Of the regular polygons, only equilateral triangles, squares, and hexagons can do this. 

Orders, then, of 3, 4, and 6.

When it comes to order 5, or 7, we need more than one polygon, and a great deal more ingenuity to make it all fit.

Order Five   -  Pentagonal Paving.

Order Seven   -  Spectral Harmonies

Cut out and Keep   -  Designs for you to copy and colour, in Orders 5, 7, 8 and 10.