Find the minimum number of straight lines needed to cover a crossing-free straight-line drawing of the icosahedron $(13\dots 15)$ and of the dodecahedron $(9\dots 10)$ (in the plane).

For example, the cube can be covered by 7 lines:

(The problem was posed 13.10.2017 by Alexander Wolff and Alexander Ravsky on page 78 of Volume 1 of the Lviv Scottish Book.

The prize for solution: *A bottle of Franconia wine!*).