What's the point group for the first tiling on that webpage? It's a periodic tiling (unlike a Penrose tiling, which is only quasiperiodic), so the crystallograp

What's the point group for the first tiling on that webpage? It's a periodic tiling (unlike a Penrose tiling, which is only quasiperiodic), so the crystallographic restriction for two dimensions says the rotation subgroup of the point group must be one of C_2, C_3, C_4 (not C_5!) or C_6: http://mathworld.wolfram.com/CrystallographyRestriction.html http://mathworld.wolfram.com/CrystallographyRestriction.html I can't tell by eye-balling it what the symmetry is for the first one, but its periodicity says it must be one of those. Quasicrystals with 5-fold symmetry are not exactly periodic. There are only 17 wallpaper groups. Since this is a wallpaper, what is its group? https://en.wikipedia.org/wiki/Wallpaper_group https://en.wikipedia.org/wiki/Wallpaper_group