Why do different crystals have different shapes and sizes?
This depends on 2 factors: 1) The internal symmetry of the crystal, and 2) The relative growth rates along the various directions in the of the crystal. For example, suppose you have mutally perpendicular axes, a, b, and c. Suppose the crystal grows at equal rates along a, b, and c, then the crystal shape will be a cube. Now suppose a different crystal grows fast in the a and b direction, but very slowly in the c direction. The crystal will then grow as thin plates with the face of the plate being perpendicular to c. These are only simple examples. More complicated cases (and shapes) happen when the crystal doesn’t have mutually perpendicular axes, and when the fastest directions of growth correspond to face or body diagonals (or even other directions) in the crystal. Why crystals grow at different rates in different directions is a very complicated question. If there is a highly attractive interaction (energetically speaking) along a certain direction of a crystal, then that direction
