Pentagonal Tilings of the Sphere and Fullerenes-like Sphere
Presented by Prof. Min YAN
Type: Oral presentation
In our attempt to classify the tilings of the sphere by geometrically congruent pentagons, we need to understand the topological aspects by ignoring the edge lengths and angles. This means the study of the embedded graph such that each cell is a pentagon. We find that most vertices should have degree 3, and the distribution of the vertices of degree > 3 has implications on the graph. Besides the application of the results to the original classification problem, the dual version of our result is also an interesting starting point for studying the fullerenes-like sphere with faces of negative curvature.