We report the discovery of 5/3, 8/5 and 13/8 periodic approximants to the quasi-periodic tiling of canonical cells with Pa3 (P213) space symmetry. Although the method–Monte Carlo optimization of the density–cannot produce quasi-periodic tiling of canonical cells, the approximants are large enough to demonstrate remarkable properties of the network, appearing as an alternative to the 3D Penrose-tiling-based models of quasi-crystals.
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