1. Sides of a dodecahedron

Hello,

I'm having a little construction problem:

Is it possible to trace all edges of a dodecahedron (or alternatively an icosahedron) with one continuing line?
So imagine a dodecahedron made up of 12 wooden pentagons. To smoothly cover up the cracks between them, I would now
like to attach a single rope along all the edges, so every edge is covered without cutting the rope. (Not preferrable: but it may
overlap once or twice if it has to.)

(Simplification of the problem)

There has to be a way to solve this problem mathematically, but I can't think of it.

Thank you very much in advance!
Greetings,
Daniel

2. Re: Sides of a dodecahedron

This is basically Euler's famous "bridges of Konigsberg" problem. The surface of a dodecahedron consists of 12 faces, each face a pentagon. Three edges meet at each vertex. If you want a single continuous line through all edges then a line through a vertex would take two of those but that leaves one edge either leading in to that vertex without any way to leave or an edge out of a vertex where your line must have started.