Short answers, pulled from the story.
Nicholas Steno discovered the law of constancy of interfacial angles in 1669. This observation established that the angles between crystal faces remain constant regardless of the crystal's size or shape. The discovery laid the groundwork for the scientific discipline of crystallography.
Max von Laue demonstrated that X-rays could be diffracted by crystals in 1912. This technique created patterns that revealed the precise arrangement of atoms within the solid. The method was further developed by William Henry Bragg and William Lawrence Bragg to analyze crystal structures with unprecedented accuracy.
Calcite and aragonite are both composed of calcium carbonate. Calcite forms a rhombohedral structure while aragonite forms an orthorhombic one. The stability of these structures depends on factors such as pressure and temperature.
The International Mineralogical Association was formed in 1959. This organization regulates the introduction of new names and ensures the rationalization of nomenclature. In July 2006, the Commission of New Minerals and Mineral Names merged with the Commission on Classification of Minerals to form the Commission on New Minerals, Nomenclature, and Classification.
Over 6,000 named and unnamed mineral species are currently recognized. The distribution of minerals is uneven with 34% of known minerals found at only one or two locations. This long tail of rarity suggests that thousands more mineral species may await discovery.