Linked from

The 3 pages that link to Crystallographic restriction theorem, each with the reason it gives.

• Space groupRelated: It explains why periodic crystals exclude fivefold rotational symmetry.

• Hexagonal crystal systemRelated: It explains why sixfold lattice symmetry is possible while fivefold symmetry is not.

• Crystallographic point groupRelated: It rules out otherwise familiar rotational orders in periodic crystals.