Batle, J.; Shutov, A. V.; Maleev, A. V. Dipole-dipole minimum energy configuration for platonic, Archimedean and Catalan solid structures. (English) Zbl 1448.78019 Phys. Lett., A 384, No. 36, Article ID 126916, 32 p. (2020). Summary: Several magnetic materials consisting of dipoles owe their properties to the specific nature of the dipole-dipole interaction. In the present work, we study systems of dipoles where the particles are arranged on various types of three-dimensional structures. However, these solids are not arbitrary. They constitute the well-known Platonic, Archimedean and Catalan solids. We systematically study them in order to fill a gap in the literature that does not contemplate this interaction in the previous solids, despite the fact that they are encountered in many different physical systems. In particular, in the regime of strong dipole moments where a classical treatment is possible, we shall provide not only the minimum energy but also the precise orientations of all their dipoles. We will numerically obtain the minimum energy configuration where all vertices possess the same classic dipole, either electric or magnetic. MSC: 78A30 Electro- and magnetostatics 74F15 Electromagnetic effects in solid mechanics 52B10 Three-dimensional polytopes Keywords:classic systems of dipoles; equilibrium configuration; minimum total energy; platonic; Arquimedean and Catalan solids PDFBibTeX XMLCite \textit{J. Batle} et al., Phys. Lett., A 384, No. 36, Article ID 126916, 32 p. (2020; Zbl 1448.78019) Full Text: DOI References: [1] Takekoshi, T., Phys. Rev. Lett., 113, Article 205301 pp. (2014) [2] Molony, P. K., Phys. Rev. Lett., 113, Article 255301 pp. (2014) [3] Shimasaki, T., Phys. Rev., 91 (2015), 021401(R) [4] Kalia, R. K.; Vashishta, P., J. Phys. C, 14, L643 (1981) [5] Bedanov, V. 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