Space-filling polyhedra

Much has been done on space-filling polyhedron (other keywords: Dirichlet domains, Voronoi cells, stereohedra, crystallography) but it's not all collected well on the Internet. What is the complete list of single space-filling convex polyhedra modulo simple deformations? Are they all known? Space filling isohedra? Space-filling polyhedra with all edge lengths equal?

A toy I would like to see is the Kelvin cell with each face magnetic to build structures with. I still cannot imagine how a shape with curved faces can fill space, or how a shape can have curved edges but flat faces. (Which is it?)