It seems to me that if a tiling is tile-uniform, then it must be vertex-uniform as well. But is this the case? How would one go about devising a proof?
By 'tile-uniform', I mean a tiling whose tile-types are the same; and a tiling which is 'vertex-uniform' is one whose vertex-types are all the same. I suppose to prove the above one would first need to look at the properties of the tile itself?
By tiling, I refer to any kind of polygon.