A Portrait of a Quadrilateral Group

Jay Zimmerman
Proceedings of Bridges 2011: Mathematics, Music, Art, Architecture, Culture (2011)
Pages 505–508 Short Papers


This paper looks at representing a group G of order 16 as a group of transformations of a compact surface of genus three. This is the surface of smallest genus upon which G can be so represented. The action is realized as a quotient of a full quadrilateral group and so all regions have four edges. This group is also NOT the group of automorphisms of a regular map. There are significant differences between this portrait and previous ones.