We introduce the notion of groups of polytope class and show that
torsion-free amenable groups satisfying the Atiyah Conjecture possess this
property. A direct consequence is the homotopy invariance of the L2-torsion
polytope among G-CW-complexes for these groups. As another application we
prove that the L2-torsion polytope of an amenable group vanishes provided
that it contains a non-abelian elementary amenable normal subgroup.Comment: 21 page