Minimum and maximum diagonal of a dodecahedron Let $s$ be the edge length of a regular dodecahedron. As a function of $s$, what is the dodecahedron's minimum and maximum diagonal (i.e. cross-section)?

Wikipedia gives the radius of the circumscribed sphere as $\frac{\sqrt{15}+\sqrt{3}}{4}s\approx 1.401s$. Your maximum diameter is twice this. It also gives the radius of the inscribed sphere as $\frac{\sqrt{250+110\sqrt{5}}}{20}s\approx 1.1135s$. Is this whatyou menant by minimum diagonal-it is between two face centers.