Optical and x-ray studies of synthetic and natural material of magnesium cordierite composition lead to the conclusion that there are five polymorphic modifications. It is proposed to restrict the name cordierite to the two pseudohexagonal forms (connected by high-low inversion relation) and to designate the two hexagonal forms as indialite (also connected by high-low inversion relation).
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Miyashiro, A., Iiyama, T., Miyashiro, T., & Yamasaki, M. (1955). The polymorphism of cordierite and indialite. American Journal of Science, 253(4), 185–208. https://doi.org/10.2475/ajs.253.4.185