Integral Apollonian Circle Packings
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Integral Apollonian circle packing defined by circle curvatures of (−1, 2, 2, 3)
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Integral Apollonian circle packing defined by circle curvatures of (−3, 5, 8, 8)
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Integral Apollonian circle packing defined by circle curvatures of (−12, 25, 25, 28)
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Integral Apollonian circle packing defined by circle curvatures of (−6, 10, 15, 19)
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Integral Apollonian circle packing defined by circle curvatures of (−10, 18, 23, 27)
If any four mutually tangent circles in an Apollonian gasket all have integer curvature then all circles in the gasket will have integer curvature. The first few of these integral Apollonian gaskets are listed in the following table. The table lists the curvatures of the largest circles in the gasket. Only the first three curvatures (of the five displayed in the table) are needed to completely describe each gasket – all other curvatures can be derived from these three.
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