The cut-and-stick nets aren't but the rest most certainly are! Look up "The Complete Book of Origami Polyhedra". I've made some of them myself: they use only square paper without tearing, cutting or sticking.
Sure it is - just a bunch of origamis stuck together.
Most of them don't have origami instructions if they have instructions at all. I didn't find any beyond a few of the platonic solids.