Closed, Open and Multi-cyclic
- Closed, open and multi-cyclic Steiner chains
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Closed Steiner chain of nine circles. The 1st and 9th circles are tangent.
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Open Steiner chain of nine circles. The 1st and 9th circles overlap.
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Multicyclic Steiner chain of 17 circles in 2 wraps. The 1st and 17th circles touch.
The two given circles α and β touch the n circles of the Steiner chain, but each circle Ck of a Steiner chain touches only four circles: α, β, and its two neighbors, Ck−1 and Ck+1. By default, Steiner chains are assumed to be closed, i.e., the first and last circles are tangent to one another. By contrast, an open Steiner chain is one in which the first and last circles, C1 and Cn, are not tangent to one another; these circles are tangent only to three circles. Multicyclic Steiner chains wrap around the inner circle several times before closing, i.e., before being tangent to the initial circle.
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