Abstract
The present study investigates the history, significance, and depiction of a polyhedron painted in the Room of Leda, as part of the decorative plan of Palazzo Balbi Senarega in Genoa, Italy, 1655.
The illusory golden oval vault is the main element in the Room of Leda, painted by Valerio Castello, with quadratura by Andrea Seghizzi. It integrates various art forms in its painted architectural structure and figurative mythological insertions. In this same room, one can observe six small stellated dodecahedra. Although an earlier representation of this polyhedron may be found in a Venetian mosaic, Johannes Kepler was the first to describe it comprehensively, in 1619.
This study formulates some hypotheses for the meaning of these representations, drawing on scientific and symbolic sources, as well as the objective evidence that the authors observed on site, revealing that the representation of these polyhedra was altered in order to achieve an ideal shape.
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Notes
- 1.
For the building’s history, with reference to the other sources [1].
- 2.
(1478–1482; Biblioteca Apostolica Vaticana, Ms. Cod. Vat. Urb. Lat. 632)
- 3.
Kepler also described the Great Stellated Dodecahedron (12 stellated pentagons, 20 vertices, and 30 edges), while in 1809, Louis Poinsot demonstrated the duality of two other non-convex regular polyhedra: the Great Dodecahedron and the Great Icosahedron.
- 4.
In 1986, this representation caught the attention of Lucio Saffaro (1970), who chose it as the symbol for the Venice Biennale [12, p. 123–125]. Moreover, the apparent contour of the drawing highlights the characteristics of this polyhedron as a three-dimensional interpretation of the five-pointed star.
- 5.
According to Gavazza [2, p. 13] this could prove that a collaborator of Valerio Castello participated in the decoration work.
- 6.
Ms. VI 6, Biblioteca Universitaria di Genova.
- 7.
Bibliothece Universitatis Genuensis Catalogus secundum auctorum Cognomina Ordine Alphabeticus dispositus, 1785-87 (Biblioteca Universitaria di Genova, Atrio Rari Ms. C. 33 1 4).
- 8.
Biblioteca Universitaria di Genova, 3 B 7 61.
- 9.
Biblioteca Universitaria di Genova, 3 LL V 43
- 10.
Biblioteca Universitaria di Genova, 3 X III 63-65
- 11.
The description by Bettini mentioned the internal pyramids of the dodecahedron. He then referred to another section of his text on the half-diameter of the circumscribed sphere, coinciding with the side of the pyramids, which is different from Kepler’s pyramids.
- 12.
The photographical survey was conducted by Cristina Càndito and Ilenio Celoria. The elaborations on the virtual model were directed by Cristina Càndito and accomplished with the collaboration of Andrea Quartara.
- 13.
ASG, Notai Antichi, Notaio Calvi Carpenini, 26.8.1649. Per la trascrizione: Montanari 2015
- 14.
Gerolamo is a son of Nicolò, brother of Pantaleone, father of Giacomo, father of Francesco Maria.
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Acknowledgments
The present study has been conducted thanks to P.R.A. 2017’s funding (Athenaeum Research Project, entitled “Representations and simulation in architecture”; scientific coordinator: C. Càndito). The paper was conceived and elaborated as a teamwork: the paragraph Observation on shadows was written by Ilenio Celoria, while the others were written by Cristina Càndito.
The authors would like to thank Lara Nicolini for the translation of the excerpt by M. Bettini, that was later interpreted by them.
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Càndito, C., Celoria, I. (2022). Scientific Sources and Representations of the Small Stellated Dodecahedra Painted in Genoa. In: Viana, V., Mena Matos, H., Pedro Xavier, J. (eds) Polyhedra and Beyond. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-99116-6_2
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