Abstract
The contribution focuses on Escher’s graphic production which includes images of polyhedra or complex geometric bodies generated by the combination of platonic solids and inspired by crystals. The Dutch artist was attracted by the sense of balance and perfection of the Platonic solids and the polyhedra derived from them. This article reviews, through conceptual graphic reworking, the geometric genesis of the compositional structure of some solids that recur in Escher’s works. The drawing allows to better understand the aggregation rules and the rigorous construction on which the sense of harmony of these solids depends. Through a graphic-geometric rereading, the authors intend to guide the observer towards a clearer interpretation of Escher’s imaginary configurations based on polyhedra. They therefore elaborate images of these solids to provide an immediate and visually effective reading of relationships and geometric correspondences. Finally, they show how extreme formal complexity equates to great simplicity in the generative matrix.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Schattschneider, D.: The mathematical side of M. C. Escher. Not. AMS 57(6), 706–718 (2010)
Escher, M.C.: Grafiek en Tekeningen, 1st edn. J.J. Till, Zwolle (1959)
Massignon, L.: Les méthodes de réalisation artistiquesdes peuples de l’Islam. Opera Minora III, 9–24 (1969)
Fedorov, E.S.: The symmetry of regular systems of figures. In: Proceedings of the Imperial St. Petersburg Mineralogical Society, vol. 28, pp. 1–146 (1891)
Pólya, G.: Uber die Analogie der Kristallsymmetrie in der Ebene. Z. Kristall 60, 278–282 (1924)
Ernst, B.: Lo specchio magico di M.C. Escher. Taschen Verlag GmbH, Köln (1996)
Schattschneider, D.: Escher’s polyhedral models. In: Proceedings of Bridges 2019. Mathematics, Art, Music, Architecture, Education, Culture, pp. 347–350. Tessellations Publishing, Phoenix (2019)
Senechal, M. (ed.): Sha** Space: Exploring Polyhedra in Nature, Art, and the Geometrical. Springer, New York (2013)
Beech, M.: Escher’s stars. J. R. Astron. Soc. Canada 86(4), 169–177 (1992)
Zefiro, L.: The compound of three octahedra and a remarkable compound of three square dipyramids, the Escher’s solid. Vis. Math. 12(3), 1–15 (2010)
Rossi, M.: Realtà e immaginazione: Nuove forme e antiche simmetrie. Disegnare Idee Immagini 38, 50–61 (2009)
Weisstein, E.W.: Cube 2-Compound. From MathWorld. A Wolfram Web Resource. https://mathworld.wolfram.com/Cube2-Compound.html. Accessed 3 July 2020
Holden, A.: Shapes, Space, and Symmetry. Dover Publications, New York (1991)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Messina, B., Chiarenza, S. (2021). Drawing and Geometric Constructions of Polyhedra in the Art of Escher. In: Cheng, LY. (eds) ICGG 2020 - Proceedings of the 19th International Conference on Geometry and Graphics. ICGG 2021. Advances in Intelligent Systems and Computing, vol 1296. Springer, Cham. https://doi.org/10.1007/978-3-030-63403-2_81
Download citation
DOI: https://doi.org/10.1007/978-3-030-63403-2_81
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-63402-5
Online ISBN: 978-3-030-63403-2
eBook Packages: EngineeringEngineering (R0)