I'll introduce a class of cusped hyperbolic 3-manifolds that we call mixed-platonic, composed of regular ideal hyperbolic polyhedra of more than one type. For reasons I'll give in the talk, we are interested in such manifolds that are complements of knots in the three-sphere. One such "knot complement" has been known for some time to fit this description; whether there are any more is an open question. I'll discuss joint work in which I and my collaborators (see below) establish basic facts about mixed-platonic manifolds which allow us to conclude, among other things, that there is no mixed-platonic hyperbolic knot complement with "hidden symmetries". In the talk I will define this term, state a conjecture due to Neumann-Reid about hidden symmetries of knot complements, and explain why one might suspect that mixed-platonic knot complements are relevant to it. I will try to make the talk accessible to a general math audience. My collaborators on this work were Eric Chesebro (U Montana), Michelle Chu (U Minnesota), Neil Hoffman (UMN-Duluth), Priyadip Mondal (former Pitt grad student, now at Ben-Gurion), and Genevieve Walsh (Tufts).