There are eight groups of symmetry properties possessed by homogeneous solids which can be distinguished from one another according to their invariance with respect to geometrical transforms. Rotational symmetry means that a body is the same after rotation (other than rotation of 2π) about a symmetry axis. Mirror symmetry exists at a plane in a body if and where the body on one side of the plane is identical to the reflection of the body on the other side.
These invariances also apply to the tensors which describe their physical properties, for example their elastic tensors, hydraulic tensors, etc. The symmetry systems may be ranked according to the number of independent elastic constants, as shown in Figure S-29. The various systems can be thought of as caused by parallel sets of cracks, though this may not be how they are created. See also anisotropy (seismic).