Proposition: Prop. 13.14: Construction of Regular Octahedron within Given Sphere
(Proposition 14 from Book 13 of Euclid's “Elements”)
To construct an octahedron, and to enclose (it) in a (given) sphere, like in the preceding (proposition), and to show that the square on the diameter of the sphere is double the (square) on the side of the octahedron.
Modern Formulation
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Notes
If the radius of the sphere is unity then the side of octahedron is $\sqrt{2}$.
Table of Contents
Proofs: 1
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Proofs: 1
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References
Adapted from (subject to copyright, with kind permission)
 Fitzpatrick, Richard: Euclid's "Elements of Geometry"
Adapted from CC BYSA 3.0 Sources:
 Prime.mover and others: "Pr∞fWiki", https://proofwiki.org/wiki/Main_Page, 2016