Binary tiling: Difference between revisions

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{{Short description|Tiling of the hyperbolic plane}}

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[[File:Binary-tiling-dual.svg|thumb|A binary tiling (red outline) and its dual tiling (yellow curved triangles and blue and green curved quadrilaterals)]]

The [[dual tiling]]s of the binary tilings are formed by choosing a reference point within each tile of a binary tiling, and connecting pairs of reference points of tiles that share an edge with each other. They isare not monohedral: the binary tilings have vertices where three or four tiles meet, and correspondingly the dual tilings have some tiles that are triangles and some tiles that are quadrilaterals. The fact that the binary tilings are non-periodic but monohedral (having only one tile shape) translates an equivalent fact about the dual tilings: they are non-periodic but ''monocoronal'', having the same pattern of tiles surrounding each vertex.{{r|fg}}

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| last2 = Schraudner | first2 = Michael

| arxiv = 2012.11037

| journal = Comptes Rendus. Mathématique Acad. Sci. Paris

| mr = 4753921

| pages = 553–580

| title = Tilings of the hyperbolic plane of substitutive origin as subshifts of finite type on Baumslag-SolitarBaumslag–Solitar groups <math>BS(1,2n)</math>

| volume = 362

| year = 2024| doi = 10.5802/crmath.571

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| volume = 293

| year = 2024| doi-access = free

| isbn = 978-3-95977-316-4

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