So, after reading up on the differences between the Kepler solids and the Poinsot solids I came up with types of regular polytopes.

1

Each face meets n at a corner where n is the number of vertices each facet has. Some examples are the tet and squat.

2

Each face meets n at a vertex where n is the number of dimensions. This means that the vertex figures are simplectic. This includes the tet, cube, and doe.

3

Each face meets n at a vertex, all faces are simplices. This includes the tet, oct, and ike.

4

Anything that's not the above. All of these are tilings.