Abstract
The schemes for division of holohedral simple forms of crystals into conjugated simple forms are derived by decomposition of the symmetry group of the primitive sublattice into double cosets. The number of equivalently oriented simple forms in the intergrowth of crystals, whose primitive space sublattices are parallel to one another, is equal to the number of holohedral permutational conjugated simple forms, which has the value 992 for all the 32 symmetry classes.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
S. F. Glinka, General Course of Crystallography (Tsinzerling, St. Petersburg, 1902).
M. Bauer, Lehrbuch der Mineralogie (Nagelel, Stuttgart, 1904).
A. V. Gadolin, Subdivisions Derivation, from a Single Common Origin, of All the Crystallographic Systems and Their Subdivisions (Izd. Akad. Nauk SSSR, Moscow, 1954; first published in Zap. Ross. Mineral. Obshchestva, Ser. 2, 4 (2), 112 (1867)).
R. V. Galiulin, Kristallografiya 23(6), 1125 (1978) [Sov. Phys. Crystallogr. 23 (6), 635 (1978)].
S. H. Chao and W. H. Taylor, Proc. Roy. Soc. London A 174, 57 (1940).
H. R. Wenk, D. J. Barber, and R. J. Reeder, Microstructures in Carbonates. Reviews in Mineralogy. Carbonates: Mineralogy and Chemistry (1983), Vol. 11, p. 301.
V. M. Vinokurov, G. R. Bulka, N. M. Nizamutdinov, and N. M. Khasanova, Dokl. Akad. Nauk SSSR 237(6), 1388 (1977).
M. Hall, The Theory of Groups (Macmillan, New York, 1959; Inostrannaya Literatura, Moscow, 1962).
O. Bravais, Etudes Cristallographiques (Gauthier-Villars, Paris, 1966; Nauka, Leningrad, 1974).
G. Ya. Lyubarskii, Group Theory and Its Application in Physics (Gostekhizdat, Moscow, 1958; Pergamon Press, Oxford, 1960).
A. V. Shubnikov, Tr. Lab. Kristallogr. Akad. Nauk SSSR 2, 3 (1940).
C. F. Nauman, Elemente der Mineralogie (Engelmann, Leipzig, 1855).
V. V. Dolivo-Dobrovol’skii, Course of Crystallography (ONTI, Leningrad-Moscow, 1937).
International Tables for Crystallography. Vol. A. Space-Group Symmetry, Ed. by T. Hahn (Reidel, Dordrecht, 1989), 3rd. ed.
P. Groth, Physikalische Krystallographie und Einleitung in die Krystallographische Kenntniss der wichtigsten Substanzen (Engelmann, Leipzig, 1876; Rikker, St. Petersburg, 1897).
R. V. Galiulin, Lectures on Geometric Foundations of Crystallography (Chelyabinsk Univ., Chelyabinsk, 1989).
R. V. Galiulin, Tr. Mat. Inst. im. V.A. Steklova, Akad. Nauk. SSSR 148, 82 (1978).
Author information
Authors and Affiliations
Corresponding author
Additional information
__________
Translated from Kristallografiya, Vol. 45, No. 4, 2000, pp. 583–590.
Original Russian Text Copyright © 2000 by Nizamutdinov, Vinokurov, Khakimov, Bulka, Galeev, Khasanova.
Rights and permissions
About this article
Cite this article
Nizamutdinov, N.M., Vinokurov, V.M., Khakimov, E.M. et al. Group-theoretical representation of holohedral forms of crystals by conjugated simple forms. Intergrowth of crystals. Crystallogr. Rep. 45, 529–536 (2000). https://doi.org/10.1134/1.1306555
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1134/1.1306555