Professor of Mathematics, Marcus du Sautoy, describes the Alhambra as the Palace of Symmetry. In the ornamentation of this Moorish fortress it is possible to discover all of the 17 symmetries that are possible on a single surface. Just as three oranges and three apples are different manifestations of the abstract number three, different wall patterns at the Alhambra can also be the expression of the same symmetry. The two patterns shown below are an example: both have the same horizontal, vertical and diagonal axis of reflection and both look exactly the same whether they are rotated 0, 90, 180 or 360 degrees. Furthermore, they can also be moved horizontally or vertically by the multiple integral of the lattice spacing. This is why they can be said to represent the same symmetry group. (abe)

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