  A family of polytopes introduced by E.M. Feichtner, A. Postnikov and B.
Sturmfels, which were named nestohedra, consists in each dimension of an
interval of polytopes starting with a simplex and ending with a permutohedron.
This paper investigates a problem of changing and extending the boundaries of
these intervals. An iterative application of Feichtner-Kozlov procedure of
forming complexes of nested sets is a solution of this problem. By using a
simple algebraic presentation of members of nested sets it is possible to avoid
the problem of increasing the complexity of the structure of nested curly
braces in elements of the produced simplicial complexes.
