MathDB

P

is a convex polyhedron such that:
(1) every vertex belongs to exactly

3

faces.
(1) For every natural number

n

, there are even number of faces with

n

vertices.
An ant walks along the edges of

P

and forms a non-self-intersecting cycle, which divides the faces of this polyhedron into two sides, such that for every natural number

n

, the number of faces with

n

vertices on each side are the same. (assume this is possible)
Show that the number of times the ant turns left is the same as the number of times the ant turn right.

Problem Statement