  Cancellative dimer algebras on a torus have many nice algebraic and
homological properties. However, these nice properties disappear for dimer
algebras on higher genus surfaces. We consider a new class of quiver algebras
on surfaces, called 'geodesic ghor algebras', that reduce to cancellative dimer
algebras on a torus, yet continue to have nice properties on higher genus
surfaces. These algebras exhibit a rich interplay between their central
geometry and the topology of the surface. We show that (nontrivial) geodesic
ghor algebras do in fact exist, and give explicit descriptions of their central
geometry. This article serves a companion to the article 'A generalization of
cancellative dimer algebras to hyperbolic surfaces', where the main statement
is proven.
