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.
How to Talk to a Liberal (If You Must) How to Talk to a Liberal (If You Must) How to Talk to a Liberal (If You Must) is a 2004 book by Ann Coulter. The book is a collection of columns written by Coulter on liberalism, the war on terror, and the media. In it, Coulter offers advice gleaned from her experience as a political pundit. She attacks "The New York Times" and the Democratic Party, and sums up her opinion of liberals in two sentences: "Want to make liberals angry? Defend the United States." In arguing with liberals, she advises, "don't be defensive", "always outrage the enemy", and