Steiner Chain - Closed, Open and Multi-cyclic

Closed, Open and Multi-cyclic

The two given circles α and β touch the n circles of the Steiner chain, but each circle C_k of a Steiner chain touches only four circles: α, β, and its two neighbors, C_k−1 and C_k+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 C_n, 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.