  The Lasserre's reconstruction algorithm is extended to the D-polytopes with
the construction of their shape space. Thus, the areas of d-skeletons $(1\leq
d\leq D)$ can be expressed as functions of the areas and normal bi-vectors of
the (D-1)-faces of D-polytopes. As weak solutions of the simplicity constraints
in all dimensional loop quantum gravity, the simple coherent intertwiners are
employed to describe semiclassical D-polytopes. New general geometric operators
based on D-polytopes are proposed by using the Lasserre's reconstruction
algorithm and the coherent intertwiners. Such kind of geometric operators have
expected semiclassical property by the definition. The consistent semiclassical
limit with respect to the semiclassical D-polytopes can be obtained for the
usual D-volume operator in all dimensional loop quantum gravity by fixing its
undetermined regularization factor case by case.
