We shall outline geometrical and algebraic ideas which appear to lie at the foundation of the theory of defective crystals that was introduced by Davini  in 1986. The focus of the paper will be on the connection between continuous and discrete models of such crystals, approached by consideration of the symmetries inherent in these models. To begin with, we review briefy the results of analysis of variational problems where relevant functionals have the symmetry of perfect (as opposed to defective) crystals, in order to motivate the subsequent study of symmetry in the case when defects are present. In the body of the paper we indicate how the theory of Lie groups, and their discrete subgroups, relates to this geometrical theory of defects, and discuss types of symmetry that occur.
Nicks, R., & Parry, G. P. Geometrical issues in the continuum mechanics of solid crystals. Miskolc Mathematical Notes,