Here is more about regular polytopes and four dimensions. For regular convex polytopes there are six regular polytopes and then for all dimensions higher than 4 there are three. For nonconvex regular polytopes there are 10 in four dimensions and zero in all higher dimensions. For convex euclidean tessellations there are 3 in four dimensions zero in all higher dimensions.
However there are some cases in which the 5th and 6th dimension have different values: For convex hyperbolic tessellations 4 in the fourth dimension, 5 in the fifth and zero in all higher dimensions. For nonconvex hyperbolic tessellations there are zero in four dimensions four in the fifth dimension and zero in all higher dimensions.
I used the wikipedia article "List of regular polytopes" which is available here as a source for the above information.
