Eighteenth-century forms of quasicrystals

A careful inspection of the drawings and baked clay models created by the mineralogist Romé de L'Isle in the 18th century has revealed the existence of a number of intriguing forms with pentagonal symmetries. These forms cannot be classified in any of the 32 crystal classes. They can thus be considered the first crystallographic descriptions of polyhedral forms found in quasicrystals two centuries later. This paper presents a symmetry analysis of the fascinating drawings and clay models with pentagonal symmetries described in the book Cristallographie published in 1783 by Romé de L'Isle, as well as a comparison with quasicrystals recently synthesized. The paper also briefly discusses what could induce Romé de L'Isle to consider forms with pentagonal symmetries as plausible crystal forms.