A
Penrose tiling is a non-periodic
tiling generated by an
aperiodic set of
prototiles. Penrose tilings are named after mathematician and physicist
Roger Penrose, who investigated these sets in the 1970s. The aperiodicity of the Penrose prototiles implies that a shifted copy of a Penrose tiling will never match the original. A Penrose tiling may be constructed so as to exhibit both
reflection symmetry and fivefold
rotational symmetry, as in the diagram at the right.