Plane of symmetry - A plane of symmetry divides a crystal into identical or mirror imaged halves. A cube has 9 planes of symmetry.
Axis of symmetry - If a crystal on being rotated comes to occupy the same position in space more than once in a complete rotation, the axis about which rotation has taken place is called an axis of symmetry. Depending upon the degree of symmetry, a crystal may comes to occupy the same position two, three, four or six times in a complete rotation. the terms aplied to these different classes of axes are as folows -
Two time - two-fold, diad
Three times - three-fold, triad
Four times - four fold, tetrad
Six times - six fold, hexad
Centre of symmetry - A crystal has acentre of symmetry when like faces, edges etc. are arranged in pairs in corresponding position on opposite sides of a central point.