Distance between centers on a dodecahedron surface

The following animation depicts unfolding of the faces of the dodecahedron. The last frame shows how to compute the distance between the two dots using two congruent triangles with two of the sides being $a$ and $2 a$ , where $a$ is the apothem of the pentagon, $a =\frac{1}{2} \cot \frac{\pi}{5}$ . And it follows that,

$d = 2 \sqrt{ 4 a^2 + a^2 - 4 a^2 \cos( \frac{4 \pi}{5} ) } = 3.950016598$ . Hence the answer is $\boxed{3950}$ .