On the Infinite Naturally Contained in the Finite

The article is devoted to the history of ideas about the shape of the crystal polyhedron and its structure. It is shown how the ideas of face belts and crystal lattice naturally introduce infinities into the science of crystals, always finite in the practice of mineralogists. The article is timed to the 2000th anniversary of the birth of Pliny the Elder, the 385th – of N. Stenon, the 280th – of R.J. Haüy, the 180th – of P.G. Groth, the 170th – of V.M. Goldschmidt, E.S. Fedorov, and A.M. Schönflies. All of them in their work tried to master the seemingly infinite varieties of objects according to found principles.