This problem is about investigating whether it is possible to start at one vertex of a platonic solid and visit every other vertex once only returning to the vertex you started at.
A description of how to make the five Platonic solids out of paper.
We are given a regular icosahedron having three red vertices. Show that it has a vertex that has at least two red neighbours.
Toni Beardon has chosen this article introducing a rich area for practical exploration and discovery in 3D geometry