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Figure 16
Density distributions for decagonal and dodecagonal quasicrystals: for these quasicrystals, γ is maximized when [{\tilde \rho}_1] = [{\tilde \rho}_q] = 1/5 or 1/8, respectively. Observe that γDEC = 4 and γDOD = 3, and note the interior Van Hove singularities at ±4/5 and −1/2, −3/8 and 0, and the zeroth-order discontinuity in the decagonal distribution at [\phi_{\min}] = −1. This final Van Hove singularity is analyzed in Section 6.5[link] and is a key factor leading to the decagonal structure's stability under the BDL model.

IUCrJ
Volume 5| Part 3| May 2018| Pages 247-268
ISSN: 2052-2525
https://doi.org/10.1107/S2052252518001161