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.
| Original language | English |
|---|---|
| Pages (from-to) | 265-283 |
| Number of pages | 19 |
| Journal | Geometriae Dedicata |
| Volume | 43 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 1992 Sep 1 |
ASJC Scopus subject areas
- Geometry and Topology
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Cite this
Ishida, M., & Kojima, S. (1992). Apollonian packings and hyperbolic geometry. Geometriae Dedicata, 43(3), 265-283. https://doi.org/10.1007/BF00151517