Oldridge, Paul Richard2017-05-012017-05-0120172017-05-01http://hdl.handle.net/1828/8030A polyhedral graph G is called PCC if every vertex of G has strictly positive combinatorial curvature and the graph is not a prism or antiprism. In this thesis it is shown that the maximum order of a 3-regular PCC graph is 132 and the 3-regular PCC graphs which match that bound are enumerated. A new PCC graph with two 39-faces and 208 vertices is constructed, matching the number of vertices of the largest PCC graphs discovered by Nicholson and Sneddon. A conjecture that there are no PCC graphs with faces of size larger than 39 is made, along with a proof that if there are no faces of size larger than 122, then there is an upper bound of 244 on the order of PCC graphs.enAvailable to the World Wide Webcombinatorial curvaturepositive combinatorial curvaturePCCpolyhedral graphpolyhedronThesis