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Next: Rotations compatible with a lattice base Up: Introduction Previous: Symmetry operations

Symmetry elements and their orientation

The symmetry element is the geometric entity around which one or more symmetry operations take place, and corresponds to the locus of the points that are left unmoved by these operations. The position of the symmetry element is obtained by solving the equation:

Ar = r

from which

(A - 1)r = 0

where 1 is the unit matrix. A solution, other than the trivial solution r = 0, can be obtained only if the condition |A - 1| = 0 is satisfied. If this does not happen, it is necessary to take into account the matrix $A \cdot A$.

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