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→Tiles: I don't think the comparison between horocyclic and polygonal tilings can be supported by sources |
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[[File:Binary tiling straight.svg|thumb|Binary tiling with [[pentagonal tiling|convex pentagon tiles]], in the Poincaré half-plane model.]]
An alternative and combinatorially equivalent version of the tiling places its vertices at the same points, but connects them by hyperbolic line segments instead of horocyclic segments, so that each tile becomes a hyperbolic convex pentagon. This makes the tiling a proper [[pentagonal tiling]].{{r|fg|kari}}
If one considers only adjacencies between tiles of different sizes, omitting the side-to-side adjacencies, this adjacency pattern gives the tiles of the binary tiling the structure of a [[binary tree]]. Representative points within each tile, connected according to this adjacency structure, give an embedding of an infinite binary tree as a [[hyperbolic tree]].{{r|kbvw}}
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