So, it's quite hard to define a polytope but I'll try.
A polytope must have flat elements (no curves), cannot have a completely concealed hole (concealed means that you cannot see it in n-1 vision where n is the number of dimensions the shape is in and isn't connected to any other element), must have polytope elements, and finally uncapped faces are only allowed when they are on an imaginary vertex which is where theoretically, is where the vertices should be on a stellation to infinity or an unbounded shape meant to have a terminating vertex but cannot as the sides are all parallel or a similar case.
What about compounds and stuff like that?
Coincidics, compounds, and combofaceteds are part of a subgroup of polytopes called combopolytopes, non combopolytopes are called monopolytopes.
Now, if you remove the flat elements part, you get what I simply call topes which can have curved elements> If they are coincidic, compounds, or combofaceted, they are called combotopes. If they aren't, then they are monotopes.