Excerpt from On Triangulations of the 3-Ball and the Solid Torus Proof 2 We use the same notation as in Proof 1. Assume A is a triangulation that con tradicts the claim. Observe that A cannot have any interior vertices. Let n fo(a). 8a is a triangulation of 2-sphere and hence satisfies Euler's relation fo(3a) f1(6a) f2(8a) 2. Also, each edge in 0a is contained in two triangles. Hence f2(3a) 2n 4. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.