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.
Many-angled ones Lanning, Quasar travels through a time/space rift to an alternate earth with multiple Lovecraftian elements being part of the everyday reality of that world. There Quasar meets the Revengers, that world's counterparts to the Avengers, who received their powers from the Many-Angled Ones in exchange for adoration and worship from the heroes. That world's Iron Man states that the Many-Angled Ones have outgrown their reality and need a new place to feed and be worshiped. They intend for Quasar to show them the way to his Earth. The Many-Angled Ones are opposed on this Earth by the heroes who believe