Stratified operations on maniplexes

There is an increasingly extensive literature on the problem of describing connection (monodromy) groups and automorphism families polytopes maniplexes that are not regular or reflexible. Many such arise as result constructions truncations products. Here we show for a wide variety these constructions, group output can be described in nice way terms input. We call operations stratified. Moreover, that, if F maniplex operation one two broad subclasses stratified operations, ℛ smallest reflexible cover some ℳ, then F(ℛ) equal to F(ℳ). In particular, this true medials maps, products (including pyramids prisms over polytopes), mix maniplexes. As application, determine covers equivelar toroidal maps.