Twelve identical circles touching one another on a sphere

This problem is related to the dodecahedron. Suppose each of 12 identical circle of flat radius $r$ to be inscribed by each of 12 congruent regular pentagonal faces of a dodecahedron with edge length $a$ . Then each pentagonal face will lie at a normal distance $h$ from the center given as $\LARGE h=r \left(\frac{1+\sqrt{5}}{2}\right)$

If we join mid-point of the edge of the dodecahedron with its center, we get a right triangle. Now, consider such a right triangle with orthogonal sides $r$ & $h$ & hypotenuse $R$ & apply Pythagoras Theorem as follows $\LARGE R=\sqrt{r^2+\left(r \left(\frac{1+\sqrt{5}}{2}\right) \right)^2}=r\sqrt{ \frac{5+\sqrt{5}}{2}}$ $\LARGE \frac{R}{r} \approx1.902$