 This is a generalization of the older category of semiregular polytopes, but also includes the regular polytopes.Further, star regular faces and vertex figures (star polygons) are allowed, which greatly expand the possible solutions.A strict definition requires uniform polytopes to be finite, while a more expansive definition allows uniform honeycombs (2-dimensional tilings and higher dimensional honeycombs) of Euclidean and hyperbolic space to be considered polytopes as well.