ISOHEDRAL TILINGS BY 8-, 10- AND 12-GONS FOR HYPERBOLIC TRANSLATION GROUP OF GENUS TWO

Abstract

As is known there are 2 types of isoheral tilings of the Euclidean plane with disks for the translation group p1. In the hyperbolic plane there exist a countable series of translation groups, each group being characterized by its genus. For the hyperbolic translation group of genus two, isohedral tilings of the hyperbolic plane with disks are studied. The technique of adjacency symbols, developed by B. N. Delone for the Euclidean case, is used. In the present article we restrict the enumeration to tilings with 8-, 10- and 12-gons.