Abstract
We study the existence of one-dimensional quasicrystal structures on the vertex set ΛP of a Penrose tiling, in an arbitrary direction . If , ζ = e2πi/5, then is a discrete family of lines that has a one-dimensional quasicrystal structure. Conversely, if w ≠ 0 and , is a dense subset of . We also have a weak analog of Kronecker's approximation theorem.
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