An ideal is described by its generators and their relations, the syzygies. Sometimes the syzygies and the free resolution they build can be described by the boundary maps of a cell complex. This is called a cellular resolution. For powers of certain edge ideals we have found a nice and descriptive way to construct these cell complexes. They are almost polyhedral complexes looking like stair-case subdivisions of simplicies, but with some extra curvy cells. We will keep the talk basic and assume nothing more than basic algebra.