  We introduce a variation of the well-known Newton-Hironaka polytope for
algebroid hypersurfaces. This combinatorial object is a perturbed version of
the original one, parametrized by a real number. For well-chosen values of the
parameter, the objects obtained are very close to the original, while at the
same time presenting more (hopefully interesting) information in a way which
does not depend on the choice of parameter.
