Kolbe, BenediktRobins, VanessaGasparovic, ERobins, VTurner, K2023-10-24978-3-030-95518-2http://hdl.handle.net/1885/303837We present a method to enumerate tile-transitive crystallographic tilings of the Euclidean and hyperbolic planes by unbounded ribbon tiles up to equivariant equivalence. The hyperbolic case is relevant to self-assembly of branched polymers. Our result is achieved by combining and extending known methods for enumerating crystallographic disk-like tilings. We obtain a natural way of describing all possible stabiliser subgroups of tile-transitive tilings using a topological viewpoint of the tile edges as a graph embedded in an orbifold, and a group theoretical one derived from the structure of fundamental domains for discrete groups of planar isometries.application/pdfen-AU© 2022 The authors202210.1007/978-3-030-95519-9_42022-08-14