The Steiner chain consists of a set of circles, which are tangent to two given non-intersecting circles and each circle in the chain is tangent to the previous and next circle in the chain. Inversion in a circle, for which we have proven some properties, translates the problem into the search of a Steiner chain between two concentric circles. We have also succeeded in finding a formula that makes it easier to check whether the Steiner chain exists and how many circles it consists of.
Through analogy in space, circles are replaced by spheres, whereas the Steiner chain is replaced by the Steiner family of spheres whose centers in concentric cases are the angles of corresponding Platonic solids. Solutions are studied through the treatment of solid angles. Here too, we have found a formula which tells us which spheres it is possible to find the Steiner family of spheres for.