Domes and Pyramids

One of our goals in this work, achieved in Theorem 4.6 , is to show that if Q can be obtained from P by sculpting, then it can also be obtained from P by tailoring.tailoringvia sculpting A key step (Lemma 4.1 ) repeatedly slices off shapes we call g-domes.g-dome Each g-dome slice can itself be achieved by slicing off pyramids,pyramid i.e., by suitable vertex truncations.truncationvertex Lemma 4.4 will show that slicing off a pyramid can be achieved by tailoring, and thus leading to Theorem 4.6 .