2023•Unpublished venueRequires access
Symmetry
Robert Melville Metzger
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Abstract
Symmetry is a property we find in objects with at least one dimension (D): (1D: symmetry of beads on a string; 2D: symmetry of objects in a plane; 3D: symmetry of objects in space). However, if this object must fill 2D or 3D space, it must meet certain local symmetry requirements, which, coupled with translational symmetry operators, allows the space to be completely filled. The symmetry operations of a certain object, or repeat unit, form a mathematical group. The Soviet literature used the Shubnikov system, which is similar to the Hermann–Mauguin system. Molecules with an internal symmetry that is not one of these 32 crystallographic point groups can form a crystal, albeit with a symmetry lower than that of the molecule. The chapter presents the transformation laws for covariant quantities. It transforms an “old” set of quantities to a “new” set of quantities, due to a transformation.