Professor, you said crystal systems are classified based on point groups (rotation and reflection symmetry) but you categorized different crystal systems only based on their rotation axes and didn't use reflection symmetry, so why did you say crystal systems are categorized based on both rotation and reflection symmetry?
You are right. I have not been entirely correct in defining systems only on the basis of pure rotation axes. One has to include roto-inversion axes also which includes as special cases the centre of inversion= 1-fold roto inversion axis and mirror plane= 2-fold roto-inversion axis. Thus the correct definition of the systems should include rotoinversion axes along with pure rotation axes. Thus I have defined monoclinic as a system having a single 2-fold axis. This is only partially correct. The correct statement should be a single 2-fold or 2-fold roto-inversion axis. Since I have not yet discussed roto-inversion axes, I was avoiding getting into that discussion. But in future, I wish to cover this topic as well.
Dear sir, as we know, the lattice is an infinite arrangement of points in space then every lattice should possess all types of symmetries. Not only just specific types. Am I right. Please help me out. TIA
Infinity has nothing to do with rotational symmetry. Only if the object comes to self coincidence after a rotation it has that rotational symmetry. So a lattice may be infinite, but if it does not come into self coincidence by a 90-degree rotation about some axis then it does not possess 4-fold symmetry. This is the case with a hexagonal lattice.
Sir... Why 5fold rotation axis is not possible???
Professor, you said crystal systems are classified based on point groups (rotation and reflection symmetry) but you categorized different crystal systems only based on their rotation axes and didn't use reflection symmetry, so why did you say crystal systems are categorized based on both rotation and reflection symmetry?
You are right. I have not been entirely correct in defining systems only on the basis of pure rotation axes. One has to include roto-inversion axes also which includes as special cases the centre of inversion= 1-fold roto inversion axis and mirror plane= 2-fold roto-inversion axis. Thus the correct definition of the systems should include rotoinversion axes along with pure rotation axes. Thus I have defined monoclinic as a system having a single 2-fold axis. This is only partially correct. The correct statement should be a single 2-fold or 2-fold roto-inversion axis.
Since I have not yet discussed roto-inversion axes, I was avoiding getting into that discussion. But in future, I wish to cover this topic as well.
Dear sir, as we know, the lattice is an infinite arrangement of points in space then every lattice should possess all types of symmetries. Not only just specific types. Am I right. Please help me out. TIA
Infinity has nothing to do with rotational symmetry. Only if the object comes to self coincidence after a rotation it has that rotational symmetry. So a lattice may be infinite, but if it does not come into self coincidence by a 90-degree rotation about some axis then it does not possess 4-fold symmetry. This is the case with a hexagonal lattice.