  We generalize the very well known boundary operator of the ordinary singular
homology theory, defined in many books about algebraic topology. We describe a
variant of this ordinary simplicial boundary operator where the usual boundary
(n-1)-simplices of each n-simplex are replaced by combinations of internal
(n-1)- simplices parallel to the faces. This construction may lead to an
infinite class of extraordinary non-isomorphic homology theories. We show
further some interesting constructions on the standard simplex.
