Ring the alarum-bell! Blow, wind! come, wrack! At least we'll die with harness on our back.

This case suggests that the alternation of a polyhedron should be bounded by actual vertex figures and alternated faces. The case of the cube is in agreement with this notion, since the alternated square is nothing.

For instance, let us suppose that Homer and Virgil, Aristotle and Cicero, Thucydides and Livy, could have met all together, and have clubbed their several talents to have composed a treatise on the art of dancing: I believe it will be readily agreed they could not have equalled the excellent treatise which Mr Essex hath given us on that subject, entitled, The Rudiments of Genteel Education.

Don't make the decision yourself and presume too much.