Crystallographic restriction theorem lattice basis, the rotation operation must map every lattice point into an integer number of lattice vectors, so the entries of the rotation matrix in the lattice basis — and hence the trace — are necessarily integers. Similar as in other proofs, this implies that the only allowed rotational symmetries correspond to 1,2,3,4 or 6-fold invariance. For example, wallpapers and crystals cannot be rotated by 45° and remain invariant, the only possible angles are: 360°, 180°, 120°, 90° or 60°. Example The general crystallographic restriction on rotations does "not" guarantee that a rotation will be compatible with a specific lattice.
Right angle to vectors. The presence of a right angle in a triangle is the defining factor for right triangles, making the right angle basic to trigonometry. A rectangle is a quadrilateral with four right angles. A square has four right angles, in addition to equal-length sides. The Pythagorean theorem states how to determine when a triangle is a right triangle. In Unicode, the symbol for a right angle is . It should not be confused with the similarly shaped symbol . Related symbols are , , and . In diagrams, the fact that an angle is a right angle is usually