(related to Proposition: Prop. 13.17: Construction of Regular Dodecahedron within Given Sphere)
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.
(not yet contributed)
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 \[\frac{\sqrt{15}-\sqrt{3}}{3}.\]
Proofs: 1