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Symmetry: Culture and Science
Volume 31, Number 4, pages 417-424 (2020)
https://doi.org/10.26830/symmetry_2020_4_417

THE ENIGMA OF THE POLYHEDRON AND FIVE-FOLD SYMMETRY IN DÜRER’S "MELENCOLIA I"

Ruslan I. Kostov^*

^* Mineralogist, crystallographer, geoarchaeologist (b. Sofia, Bulgaria, 1956).
Address: Department of Mineralogy and Petrography, University of Mining and Geology “St. Ivan Rilski”, “Prof. Boyan Kamenov” Street, Sofia 1700, Bulgaria.
Fields of interest: mineralogy, gemmology, archaeomineralogy, applications of symmetry, history of science.
E-mail: rikostov@yahoo.com

Publications: with Kostov, I. (1988) On the tabular presentation of the crystallographic and finite symmetry groups, Comptes Rendus de l’Académie Bulgare des Sciences, 41, 4, 45-47; with Kostov, I. (1988) On the fivefold cluster symmetry, Crystal Research and Technology, 23, 8, 973-977; with Kostov, I. (1989) Infinite symmetry applied to crystals and crystal aggregates, Crystal Research and Technology, 24, 9, 847-852; (1995) Geology beyond nature: symmetry cases in culture, Symmetry: Culture and Science, 6, 2, 312-315; (2014) Pentagon-dodecahedral and icosahedral artifacts in antiquity: 3D five-fold symmetry applied to cultural heritage, Annual of the University of Mining and Geology “St. Ivan Rilski”, 57, 4, 23-27.

Abstract: The engraving “Melencolia I” (1514) by the German artist Albrecht Dürer (1471-1528) is studied from a symmetry point of view. A review is made on the interpretation of the enigmatic polyhedron or crystal, one of the key elements of the composition, in comparison with some of the artist’s geometrical sketches and a preliminary mirror symmetry drawing. Five-fold symmetry is suggested both for the polyhedron and specific angles or proportions, linked to the correspondent golden section.

Keywords: symmetry, polyhedron, crystal, Dürer, "Melencolia I"

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