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Da Vinci's Polyhedra

Divinely illustrated polyhedra

Da Vinci briefly studied geometry with Pacioli, but was primarily interested in their descriptive features and with representing them artistically. Da Vinci produced 60 plates of polyhedral illustrations for Pacioli's work De divina proportione.

Da Vinci's Polyhedra

Italian mathematician and Franciscan friar Luca Pacioli was a polyhedron enthusiast who studied their properties and constructed many wooden models. Leonardo da Vinci produced 60 plates of polyhedral illustrations for Pacioli's work De divina proportione about mathematical and artistic proportion, written in Milan in 1496–1498 and published in Venice in 1509. Most of da Vinci's illustrations occur in pairs of contrasting models: one with solid faces and the other with solid edges. These are the first illustrations of polyhedra represented using solid edges. Just two copies of the original manuscript are known: one sits in the Biblioteca Ambrosiana in Milan, while the other is housed in the Bibliothèque de Genève.

Artifact dimensions

285 mm × 200 mm

Artifact origin

Milan, Italy

Current artifact location

Biblioteca Ambrosiana, Milan; Bibliothèque de Genève Central

Catalog number

& 170 sup. (S.P.6)


Polyhedra timeline Burnt City Dice Euclid's Elements Pottery Sherd Icosahedron Construction Serpentinite Icosahedral Die Icosahedral Die with Divine Entities Da Vinci's Polyhedra Kepler's Planetary System

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Other Resources

Additional Reading

  • Livio, M. The Golden Ratio: The Story of Phi, The World's Most Astonishing Number. New York: Broadway Books, pp. 128–137, 2002.
  • Pacioli, L. De divina proportione. Venice, Italy: Paganino Paganini, 1509.
  • Pacioli, L. De Divina Proportione. Ciniselllo Balsamo, Italy: Silvana Editoriale, 1982.
  • Pacioli, L. De divina proportione: (On the Divine Proportion): Facsimile in Full Color of the Original Version of 1509. Leopold Publishing, 2014.
  • Pappas, T. The Joy of Mathematics: Discovering Mathematics All Around You. San Carlos, CA: Wide World Publishing/Tetra, p. 81, 1989.
  • Hart, G. Shaping Space: Exploring Polyhedra in Nature, Art, and the Geometrical Imagination (Ed. M. Senechal). Springer, pp. 125–127, 2013.