Recent work on discrete classical problems in one-dimensional statistical mechanics has shown that, given certain elementary symmetries, such problems may not have a periodic (crystalline) ground state, even in the absence of fine tuning of the couplings. Here these results are applied to several families of well known polytypic materials. The families studied are those represented by the compounds SiC, CdI(2) and GaSe, and also the micas and kaolins. For all families but SiC, it is found that there is a finite probability for the ground state to be degenerate and disordered.