Tilings of the Sphere by Almost Equilateral Pentagons

The event is taking part on the Thursday, Sep 19th 2019 at 15.30
Theme/s: Pure Maths
Location of Event: 306 Alan Turing
This event is a: Public Seminar

The classification of tilings of the sphere by congruent pentagons can be divided into three cases: variable edge length, equilateral, and almost equilateral. The first two cases have been largely settled by Min Yan and his collaborators. The almost equilateral pentagon case is the most difficult and techniques developed for the other two cases are not enough.

In this talk, we will talk about full classification of this case with three distinct angles and the complete classification of five distinct angles under the assumption of the existence of a special tile. We will explain the new techniques developed and how they fit into the classification programme. We will also discuss how tilings by combinatorial pentagons play a role in a geometric realisation problem proposed by Michel Deza. This talk is based on the joint work with Min Yan, The Hong Kong University of Science & Technology, and Yohji Akama, Tohoku University, Japan.

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External Speakers

Hoi Ping Luk (Hong Kong University of Science and Technology)