Antonio Breda d'Azevedo

University of Aveiro

# Regular Map Representations

#### Abstract

This talk is a tribute to Lynne James's work on map representations. The Walsh bipartite map and Vince's 2-face bipartite map are just two regular map representations of hypermaps, being the first one the most known. These are just two examples of 'thin' regular representations, others are less familiar. Restrictedly-marked maps are used to classify the 'thin' regular maps representations of hypermaps. Stepping up on dimension, there exists a nice and natural, though 'non-thin', regular map representation of n-polytopes, n-hypertopes, and the more general n-maniplexes and n-hyperplexes introduced by Wilson.

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