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Penrose Tilings and Wieringa Roofs

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display edges
transparent tiles
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color rhombi differently
Traditionally, the P3 Penrose tiling is made of thin and thick rhombi. However, by raising the vertices in three dimensions, it is possible to force all of the rhombi to be congruent. The resulting surface is known as a Wieringa roof. Due to similarities with three-dimensional quasicrystals, you can see rhombic triacontahedra and hexecontahedra hidden in the tiling.
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