3 ms·
"The groups of atoms in crystals repeat at regular intervals, just like the five known patterns." What is "five known patterns" a reference to? I found [1] bu
by ken 8y ago
"The groups of atoms in crystals repeat at regular intervals, just like the five known patterns."
What is "five known patterns" a reference to? I found [1] but I don't see five of anything here.
[1]: https://en.wikipedia.org/wiki/Crystal_structure https://en.wikipedia.org/wiki/Crystal_structure
- kkylin 8y agoI assumed that he was talking about the possible point groups in 2d (since his demo was a slide). In 2d lattices, the possible point groups are cyclic groups of order 2,3,4,6. Cyclic groups of order 5 cannot occur; one consequence is that regular pentagons cannot tile the plane. See https://en.wikipedia.org/wiki/Crystallographic_point_group https://en.wikipedia.org/wiki/Crystallographic_point_group and https://en.wikipedia.org/wiki/Crystallographic_restriction_theorem https://en.wikipedia.org/wiki/Crystallographic_restriction_t.... I should add that I know nothing about crystallography, and am relying on decades-old knowledge from the last abstract algebra class I took.
- ebcode 8y agoThe Platonic Solids: https://en.wikipedia.org/wiki/Platonic_solid https://en.wikipedia.org/wiki/Platonic_solid
- pdonis 8y agoNot all of those correspond to patterns of crystal structure (although some do: tetrahedron, cube, and octahedron, IIRC).
- jacobolus 8y agoQuasicrystals are based on the symmetry system of the icosahedron/dodecahedron, in which it it is impossible to periodically tile space. “Proper” crystal structures are periodic, and are not necessarily related to any Platonic solid. See https://en.wikipedia.org/wiki/Crystal_system https://en.wikipedia.org/wiki/Crystal_system (but I’m not quite sure where the 5 comes from in TFA).