Table 1 Inflation factors of type IA tilings with 1 ≤ n ≤ 5 and n ≤ m ≤ n + 6a
From: Metallic-mean quasicrystals as aperiodic approximants of periodic crystals
m | n | ||||
|---|---|---|---|---|---|
1 | 2 | 3 | 4 | 5 | |
n | \(\frac{{{\mathbf{3}} + \sqrt {{\mathbf{13}}} }}{{\mathbf{2}}}\) | \(2 + \sqrt 6 \) | \(\frac{{5 + \sqrt {37} }}{2}\) | \(3 + \sqrt {13} \) | \(\frac{{7 + \sqrt {69} }}{2}\) |
n + 1 | \(2 + \sqrt 3 \) | 5 | \({\mathbf{3 + }}\sqrt {{\mathbf{10}}} \) | \(\frac{{7 + \sqrt {57} }}{2}\) | \(4 + \sqrt {19} \) |
n + 2 | \(\frac{{5 + \sqrt {13} }}{2}\) | \(3 + \sqrt 7 \) | \(\frac{{7 + 3\sqrt 5 }}{2}\) | 8 | \(\frac{{{\mathbf{9 + }}\sqrt {{\mathbf{85}}} }}{{\mathbf{2}}}\) |
n + 3 | 5 | \(\frac{{7 + \sqrt {33} }}{2}\) | \(4 + \sqrt {13} \) | \(\frac{{9 + \sqrt {73} }}{2}\) | \(5 + 2\sqrt 6 \) |
n + 4 | \(\frac{{7 + \sqrt {21} }}{2}\) | \(4 + \sqrt {10} \) | \(\frac{{9 + \sqrt {61} }}{2}\) | \(5 + \sqrt {21} \) | \(\frac{{11 + \sqrt {109} }}{2}\) |
n + 5 | \(4 + \sqrt 7 \) | 8 | \(5 + 3\sqrt 2 \) | \(\frac{{11 + \sqrt {97} }}{2}\) | \(6 + \sqrt {31} \) |
n + 6 | \(\frac{{9 + \sqrt {37} }}{2}\) | \(5 + \sqrt {15} \) | \(\frac{{11 + \sqrt {85} }}{2}\) | \(2(3 + \sqrt 7 )\) | \(\frac{{13 + \sqrt {141} }}{2}\) |
