I 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 o

I 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.