Apollonian packings and hyperbolic geometry |
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Authors: | Minoru Ishida Sadayoshi Kojima |
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Affiliation: | (1) Department of Information Science, Tokyo Institute of Technology, Ohokayama Meguro, 152 Tokyo, Japan |
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Abstract: | We review the generalized apollonian packings by Bessis and Demko from 3-dimensional viewpoints and solve their conjectures on the discreteness of the groups they constructed. Moreover, we systematically generalize the construction of packings in terms of the Coxeter group theory, and propose a computational algorithm to draw the pictures efficiently based on the automatic group theory. |
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