In recent years the problem of obtaining a reversible discrete surface polyhedrization (DSP) is attracting an increasing interest within the discrete geometry community. In this paper we propose the first algorithm for obtaining a reversible polyhedrization with a
, i.e., together with a bound on the ratio of the number of facets of the obtained polyhedron and one with a minimal number of facets. The algorithm applies to the case of a
DSP when a discrete surface
is determined by a convex body in ℝ
. The performance estimation is based on a new lower bound (in terms of the diameter of
) on the number of 2-facets of an optimal polyhedrization. That bound easily extends to an arbitrary dimension
. We also discuss on approaches for solving the general 3D DSP.