To construct an icosahedron and comprehend it in a sphere, as in the case of the aforesaid figures; and to prove that the side of the icosahedron is the irrational straight line called minor.
Proof
Inscribe a regular pentagon in a circle (IV.11); arrange two parallel
pentagons rotated 36∘ from each other, plus two apex points.
Twelve vertices form the icosahedron. The side is a minor straight
line by XIII.11.