Crystallography, Group Theory, Etymology, and ‘Pataphysics

Duparc discusses the relations between crystallograpy, group theory, mainly from an historical and etymological point of view. Crystallography existed long before 1912. It started when the French mineralogist Rene-Just Hauy designed geometrical models with tentative microscopic physical units in order to generate a global explanation of the various observations of the external shapes of crystals available in his time (18th century), what one may call a physico-mathematical theory. Maybe more than physics and chemistry, these early advances involved developments in geometrical symmetry considerations. Some of them have been done independently of equivalent developments made in algebraic structures dealing with the roots of polynomial equations.