The limiting case is when A, B and C are all the same size. The hexlet now becomes straight. "S"1 is small as it passes through the hole between A, B and C, and grows till it becomes a plane tangent to them. The centre of inversion is now also with a point of tangency with the image of "S"6, so it is also a plane tangent to A, B and C. As "S"1 proceeds, its concavity is reversed and now it surrounds all the other spheres, tangent to A, B, C, "S"2 and "S"6. "S"2 pushes upwards and grows to become a tangent plane and "S"6 shrinks. "S"1 then obtains "S"6's former position as a tangent plane. It then reverses concavity again and passes through the hole again, beginning another round trip. Now the line of centres is a degenerate hyperbola, where it has collapsed into two straight lines.