Census of quadrangle groups inclusions - d’Azevedo, António Breda (2016)
In a classical result of 1972 Singerman classiﬁes the inclusions between triangle groups. We extend the classiﬁcation to a broader family of triangle and quadrangle groups forming a particular subfamily of Fuchsian groups. With two exceptions, each inclusion determines a ﬁnite bipartite map (hypermap) on a 2-dimensional spherical orbifold that encodes the complete information and gives a graphical visualisation of the inclusion. A complete description of all the inclusions is contained in the attached tables.