What is the maximum number of edges we can select from a regular dodecahedron so that no two of them have a common point?
If no two selected edges have a common point, then from any vertex of the polyhedron, at most one selected edge can start. Therefore, we can select at most as many edges as the polyhedron has vertices. Each edge contains two vertices - its two endpoints. The dodecahedron has 20 vertices, so we cannot select more than 10 edges.

# $1988-02-076-2 . e p s$ 

However, we can select 10 edges in the required manner. For this, consider two opposite, parallel faces of the regular dodecahedron and the 10 edges that have exactly one endpoint on one of the two selected faces. These 10 edges clearly meet the conditions, as all 20 vertices of the dodecahedron appear among their endpoints.