Roger Penrose – Forbidden crystal symmetry in mathematics and architecture

Sir Roger Penrose provides a unique insight into the “forbidden symmetry” of his famous penrose tiles and the use of non-repeating patterns in design and architecture.

It is a rigorous mathematical theorem that the only crystallographic symmetries are 2-fold, 3-fold, 4-fold, and 6-fold symmetries.

Yet, since the 1970s 5-fold, 8-fold, 10-fold and 12-fold “almost” symmetric patterns have been exhibited, showing that such crystallographically “forbidden symmetries” are mathematically possible and deviate from exact symmetry by an arbitrarily small amount. Such patterns are often beautiful to behold and designs based on these arrangements have now been used in many buildings throughout the world.

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