This symmetry system has got to be my least favourite of all seventeen groups. Four different mirrors forming a box. Ew. The House of Mirrors in horror movies. It can be useful if you’re trying to tessellate four different characters that all have bilateral symmetry.
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Surprisingly, I never would have thought that this symmetry group would end up being a favourite. A tight area where a 6-fold rotation occurs, at the corner of a triangle. The other two corners offer 3 way rotation and 2 way rotation. This repeated 6 times in a hexagon. This is the nerdy way to explain it, not really the best way. Twenty five in the slideshow below!
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Tessellations by Francine Champagne 