Abstract

A recently suggested geometrical embedding of Bethe-type lattices (branched polymers) in the hyperbolic plane [R. Mosseri and J. F. Sadoc, J. Phys. Lett. 43, L249 (1982); J. A. de Miranda-Neto and F. Moraes, J. Phys. I. France 2, 1657 (1992)] is shown to be only a special case of a whole continuum of possible realizations that preserve some of the symmetries of the Bethe lattice. The properties of such embeddings are investigated and relations to Farey trees, devil's staircases, and Apollonian tiling are pointed out.

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