◀ ▲ ▶Branches / Geometry / Elements-euclid / Book-13-platonic-solids / Corollary: Cor. 13.17: Construction of Regular Dodecahedron within Given Sphere

Corollary: Cor. 13.17: Construction of Regular Dodecahedron within Given Sphere

(related to Proposition: Prop. 13.17: Construction of Regular Dodecahedron within Given Sphere)

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

So, (it is) clear, from this, that the side of the dodecahedron is the greater piece of the side of the cube, when it is cut in extreme and mean ratio (Which is) the very thing it was required to show.

Modern Formulation

(not yet contributed)

Notes

If the radius of the circumscribed sphere is unity then the side of the cube is $\sqrt{4/3}$, and the side of the dodecahedron is \[\frac{\sqrt{15}-\sqrt{3}}{3}.\]

Table of Contents

Proofs: 1

Mentioned in:

Proofs: 1
Propositions: 2

Thank you to the contributors under CC BY-SA 4.0!

Github:

non-Github:

@Fitzpatrick

References

Adapted from (subject to copyright, with kind permission)

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