Elements of symmetry of the organic world - under this title was published in 1925, the first article by D.V.Nalivkin on curvilinear symmetry ...

Distorted crystal forms, as repeatedly noted in the literature, are peculiar indicators of the symmetry of the crystal-forming medium. They include forms with reduced symmetry, (but compared to the true symmetry of a given crystalline substance), which are combinations of parts of the true prossive forms in the form of aggregates of faces connected by elements of the external (visible) symmetry of the crystal ...

The names of simple crystallographic forms, proposed in 1924 on the initiative of Prof. A.K.Boldyrev by Fedorov Institute, have been widely spread and recognized. This is evidenced by the statement of famous foreign crystallographers I.D.H. Donnaya and H. Kurien, who spoke at the Committee on Nomenclature of the French Mineralogical and Crystallographic Society in 1958: “The principles on which a satisfactory terminology of forms should be based are known. We owe this mainly to Grote and the crystallographers of the Fedorovsky Institute <...>. The nomenclature described here is used with some minor variations in the languages: German, English, Spanish, Italian, Dutch, Russian” ....

The general doctrine of symmetry owes much of its development to crystallographers and mineralogists who worked within the walls of the Leningrad Mining Institute. First of all, we should recall the achievements of the brilliant scientist E. S. Fedorov (1853-1919).

The practical significance of the crystallographic varieties of simple forms deduced by G. B. Bokii [1940] became evident after the derivation of the twin laws.

One of the pressing issues of today is the introduction of mathematics in the field of geological and mineralogical sciences. In this connection it is instructive to trace on the example of crystallography, how from a purely descriptive natural history discipline, closely related to mineralogy, grew the modern science of crystals, which is characterized above all by a strictly mathematical character. One of the greatest crystallographers who put crystallography, in the words of A. K. Boldyrev, “... firmly, invariably and irrevocably on an exact mathematical, geometrical basis”, was the world-famous professor and director of the St. Petersburg Mining Institute (now the Leningrad Mining Institute) E. S. Fedorov (1853-1919). His outstanding pupil A. K. Boldyrev (1883-1946) and even later the most talented representative of the Fedorov school V. I. Mikheev (1912-1956) worked successfully in the same direction. They made a significant contribution to the development of the mathematical foundations of modern crystallography, forever linking the history of this science with the history of the Leningrad Mining Institute ...

Re-reading Lomonosov's famous works - the treatise “On the Layers of the Earth” (1763) and “Word about the birth of metals from the shaking of the Earth” (1757), each time unexpectedly discover in them new details not noticed before, as if responding to the most burning questions of geological science of today. This has been repeatedly noted by the researchers of the great scientist's work. V.I. Vernadsky wrote: “In 1901 there was no geochemistry in our understanding and it was impossible to consider Lomonosov's thought from this point of view...”. On the amazing gift of Lomonosov's scientific foresight in the field of crystal structure it was written: “It is characteristic that as early as 1911. B. N. Menshutkin wrote about such a remarkable from the modern point of view Lomonosov's dissertation (“On the birth and nature of saltpeter”, 1749): “This dissertation I do not cite, as there is nothing interesting in it.” Only the discovery of X-ray diffraction in crystals (1912) and the subsequent rapid development of the latest structural crystallography revealed the full significance of Lomonosov's statements...” ...

Изучая научные труды В. И. Михеева, прежде всего поражаешься исключительной целеустремленностью и четкостью основной линии его творчества. Эта линия — прямое продолжение и развитие трудов его учителя А. К- Болдырева, а тем самым и трудов Е. С. Федорова. Вот почему в наших глазам В. И. Михеев является выдающимся представи­телем федоровской школы, кристаллографо-минералогической школы Горного института. Чтобы проследить определяющие иерты творческого пути В. И. Ми­хеева, необходимо вспомнить некоторые характерные моменты из его биографии.

Простые реберные формы тригональной и гексагональной сингоний. Для кристаллов тригональной и гексагональной сингоний нами выве­дено 90 простых реберных форм. В целях их классификации вос­пользуемся нумерацией и специальными символами, принятыми для тет­рагональных форм.

В настоящее время закончена разработка универсального геометри­ческого учения о формах кристаллов как обычных, так и усложненных (кристаллических скелетов, пирамид роста, индукционных поверхностей, закономерных сростков и т. д.)

St. Petersburg (now Leningrad) Mining Institute even before the Great October Socialist Revolution was one of the centers of crystallography and mineralogy, widely known not only in our country, but also throughout the world. In the last century, the works of two founders of the descriptive crystallographic-mineralogical school in Russia - famous professors of the Institute - Academician N. I. Koksharov (1818-1892) and Academician P. V. Eremeev (1826-1899) were universally recognized. Since 1905, the chairs of crystallography and petrography were headed by E. S. Fedorov (1853-- 1919), an outstanding pupil of the Institute; mineralogy was taught by his pupil and assistant V. V. Nikitin (1867-1942), the author of the famous monograph “Fedorov's Universal Method”. New crystallographic, mineralogical and petrographic methods developed at the Institute, based on the remarkable Fedorov discoveries and achievements, attracted numerous students not only from all parts of our homeland, but also from abroad. T. Barker from Oxford, L. Duparc from Geneva, Jimbo from Japan and a number of other major foreign specialists spent several years in Russia learning crystallochemical analysis and universal method from their creator, E. S. Fedorov.

The "Journal of the Leningrad Mining Institute during the fifty years of its existence occupy a prominent role in the history of the development of Russian mineralogy and crystallography. From the beginning of the foundation of the journal and to the end of his life one of the most active workers of the Notes was the famous professor and director of the Mining Institute, the greatest Russian crystallographer, geometer, petrographer, and mineralogist E. S. S. Kovalov. С. Fedorov (1853-1919). From 1907 to 1917, 144 of his works appeared in the pages of the Notes. Of these, 65 are related to crystallography proper, 4 to mineralogy and 5 to petrography. The remaining articles treat mainly questions of new geometry, intensively developed in those years by the scientist. However, in these seemingly purely geometric works E. S. Fedorov paid special attention to the practical use of his theoretical conclusions in the field of crystallography, mineralogy and mining. Thus, for example, in the article “Precise representation of points of space on the plane” (1907, vol. I, vol. 1, issue 1) various ways of representing points of three-dimensional space on the plane with the help of circles (vectoral and ordinary) and parallel vectors are proposed. In the article “Representation of Crystal Structure by Vectorial Circles” (1908, vol. I, vol. 4), the mentioned methods were successfully applied to represent elementary particles composing spatial crystal structures on the plane. This remarkable method was recalled by A. N. Zavaritsky and demonstrated its efficiency on examples of the image of real crystal structures.

From the establishment of the connection between the external shape of a crystal and its structure, as is known, all modern crystal chemistry was born: before the development of X-ray structural analysis, information about the structure of crystals was based solely on the external shape and cleavage.

The method of calculating network densities, previously used in crystal chemical analysis, gives results that do not coincide with the results for the real structure, due to the fact that we are dealing not with one, but with several parallelepipedal systems of points inserted into each other. This circumstance was already noted by E. S. Fedorov himself in his article “On the question of determining the density of atoms in the faces of crystals.” However, Fedorov’s method for calculating grid densities can be used not only for individual parallelepipedal lattices, but also in the presence of a structure that forms lattices similar to the above-described “pseudo-octahedral” one, to calculate geometric atomic grid densities.