| Issue |
E3S Web Conf.
Volume 627, 2025
VI International Conference on Geotechnology, Mining and Rational Use of Natural Resources (GEOTECH-2025)
|
|
|---|---|---|
| Article Number | 01004 | |
| Number of page(s) | 7 | |
| Section | Geology, Geophysics and Geotechnology | |
| DOI | https://doi.org/10.1051/e3sconf/202562701004 | |
| Published online | 16 May 2025 | |
Geometric interpretation of Bravais lattices
1 Moscow State University of Civil Engineering, Moscow, Russian Federation
2 Saratov State University of Genetics, Biotechnology and Engineering named after N.I. Vavilov, Saratov, Russian Federation
3 Bukhara State Pedagogical Institute, Bukhara, Uzbekistan
4 Saint-Petersburg State University of Industrial Technologies and Design, Saint Petersburg, Russian Federation
5 Saint Petersburg State University of Architecture and Civil Engineering, Saint-Petersburg, Russian Federation
* Corresponding author: sokolova_vika@inbox.ru
The study presents the results of the analysis of two-dimensional hexagonal Bravais lattices in regular packings of arbitrary congruent geometric objects on a plane. For computer modeling, three geo-metric objects of different shapes were used in the study. The relationships between four types of congruent representations in a regular packing of geometric objects on a plane are shown. The transformations of rotation of objects by 1800, transformations of mirror symmetry, as well as a joint trans-formation of mirror symmetry and rotation of objects by 1800 are considered. The use of cognitive visualization allowed us to identify two common properties of regular packings of arbitrary congruent geometric objects on a plane. The first property is related to the fact that any object of a dense regular packing of similarly oriented objects has a tangency with six surrounding objects, forming a honeycomb structure. The analysis of the pole hexagon led to the heuristic judgment that the basis of two-dimensional hexagonal Bravais lattices of regular packings similarly oriented are affine-regular hexagons. The possibility of forming regular packings in which the geometric objects of each row have different types of congruence is shown.
© The Authors, published by EDP Sciences, 2025
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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