Mirror Combination Scheme in Direct Lattice

In the first two chapters, we studied some important conceptual aspects of plane mirrors and the formation of different types and numbers of images with same or different handedness. Also, the mathematical formulation of intersecting mirrors was used to generate rotational and inversion symmetries. Further, 2 (1-D), 10 (2-D) and 32 (3-D) point groups have been determined using mirror combination scheme to justify the fundamental nature of mirror symmetry. Also, making use of a newly developed concept of minimum symmetry form (MSF) or point groups minima (PGM), it has been possible to make some inevitable changes in the wrongly allotted point groups in low symmetry crystal systems, such as oblique and rectangular in 2-D and triclinic, monoclinic and orthorhombic in 3-D.