Polyhedra and polytopes23 of 113
Platonic solids
Theaetetus; Euclid, Elements XIII
Convex solids whose faces are identical regular polygons, with the same number meeting at every corner. The last book of Euclid’s Elements proves there are only five. Plato, writing a century before Euclid, matched four of them to the elements and the dodecahedron to the heavens.
{p, q}: {3,3} {4,3} {3,4} {5,3} {3,5}
On mathcurve.com as Solides de Platon
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In the library
2
Divina proportioneLeonardo da VinciJune 1, 1509Metropolitan Museum of Art, New York, NY Pacioli’s Divina proportione of 1509, with Leonardo’s drawings of the regular solids both filled and as open frames. The page reproduced here is one of Pacioli’s capital letters, not a solid.
Not yet checkedSuggested by an AI model, 2026-10-08Source
An AI reviewer agreed, 2026-10-09: The source page says "Leonardo drew the illustrations of the regular solids while he lived with and took mathematics lessons from Pacioli," and its third part covers the Five Regular Solids, which are the Platonic solids. The picture is a capital M built with ruler and compass, as the note says, so it does not show a solid, though the text only names the open-frame drawings and does not mention filled ones.
Underweysung der Messung (Nuremberg, 1538)Albrecht Dürer1538, 1527, 1532Metropolitan Museum of Art, New York, NY Book four of Dürer’s treatise prints the regular solids as nets, flat drawings to cut out and fold, the first nets ever published. The page reproduced here is not one of them.
Not yet checkedSuggested by an AI model, 2026-10-08Source
An AI reviewer had doubts, 2026-10-09: The source says "An early instance of polyhedral nets appears in the works of Albrecht Dürer" and that his book included nets for the Platonic solids, which supports the link. It does not say they were the first nets ever published, and it never names book four, so the note claims more than the evidence shows. The reproduced page does show column plans and German text about Vitruvius rather than nets, as the note says.
Elsewhere
1Work the library cites and does not hold: in copyright, never released as a file, or not a file at all. The cited shelf
- 1955
The Sacrament of the Last Supper
The supper takes place inside a vast transparent dodecahedron. Dalí tied its twelve pentagonal faces to the twelve apostles, and the gallery reads the enclosure as the room of the scene.
Not yet checkedSuggested by an AI model, 2026-10-08
An AI reviewer had doubts, 2026-10-09: The article supports the dodecahedron setting, saying "The scene's setting is within a transparent dodecahedron", but nothing in the evidence says Dalí tied its twelve faces to the twelve apostles. The gallery's own reading could not be read, so that part of the note is unsupported.