  Generalized M\"obius-Listing bodies and surfaces are generalizations of the
classic M\"obius band. The original motivation is that for solutions of
boundary value problems the knowledge of the domain is essential. In previous
papers cutting of GML bodies with cross section symmetrical disks with symmetry
2, 3, 4, 5 and 6 have been classified. In this paper we solve the general case,
using regular m-gons as cross section. The 3D problem is reduced to the problem
of cutting regular m-polygons with d-knives, related to the number of divisors
of m. The problem has both a geometrical and topological solution, and has many
connections to other fields of mathematics.
