Proposition: Prop. 13.17: Construction of Regular Dodecahedron within Given Sphere

(Proposition 17 from Book 13 of Euclid's “Elements”)

To construct a dodecahedron, and to enclose (it) in a sphere, like the aforementioned figures, and to show that the side of the dodecahedron is that irrational (straight line) called an apotome.

Modern Formulation

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Proofs: 1 Corollaries: 1

Proofs: 1

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Adapted from (subject to copyright, with kind permission)

  1. Fitzpatrick, Richard: Euclid's "Elements of Geometry"

Adapted from CC BY-SA 3.0 Sources:

  1. Prime.mover and others: "Pr∞fWiki",, 2016