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.
I haven’t properly started yet; my friend just lent them to me recently and I’ve intermittently read a few pages and thumbed through out of curiosity. I’m excited to actually dig into it and focus less on other reading.