In this talk, I'll motivate a technique called "clique replacement" that produces a new polytope from an existing one. I will then outline an upcoming REU project based on the new technique. ("REU" stands for Research Experience for Undergraduates.) The project has several components - some involve traditional proofs, others are computer-based searches or experiments. Since the project is upcoming, this informal talk will mostly present questions rather than provide answers. The talk should be broadly accessible but anyone not knowing the definition of a polytope's face lattice is encouraged to attend the pre-talk.