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Oct 8, 2022 at 0:41 comment added uhoh in that case you may also find interesting Proposing a 2D quasicrystal; what are the necessary and sufficient conditions? (If it looks like a duck and quacks like a duck, or...?)
Oct 8, 2022 at 0:32 comment added Oscar Lanzi Yes. Four indices are used for hexagonal crystals for convenience. Three would have been enough mathematically. In contrast, with the advent of quasicrystals we now have some crystals that mathematically require as many as six indices!
Oct 8, 2022 at 0:24 comment added uhoh My understanding is that even in this crystal system three indices is sufficient mathematically but the fourth is added for convenience, e.g. "Thus four indices are commonly used for that case." Have I got that right? Also, an outstanding (as in currently unanswered) question in Matter Modeling SE: Straightforward formalism to get four sets of 2D hexagonal lattice vectors of fcc(111) planes that I can also cite?
Jan 16, 2021 at 19:39 history edited Oscar Lanzi CC BY-SA 4.0
Chasing typos.
Jan 15, 2021 at 3:28 history edited Oscar Lanzi CC BY-SA 4.0
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Jan 10, 2021 at 20:54 history edited Oscar Lanzi CC BY-SA 4.0
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Jan 10, 2021 at 20:41 history edited Oscar Lanzi CC BY-SA 4.0
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Jan 10, 2021 at 11:22 history edited Oscar Lanzi CC BY-SA 4.0
Added a clarification.
Jan 10, 2021 at 11:17 history edited Oscar Lanzi CC BY-SA 4.0
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Jan 10, 2021 at 11:11 history answered Oscar Lanzi CC BY-SA 4.0