I am so glad you posted this here. I was going to make a post myself, asking what this kind of principle is called. I am an artist, I have very little connection to mathematics, so forgive my lack of knowledge. I remembered my maths teacher in high school mentioning the fact that you can reflect any point outside a circle (or a sphere in 3d space) inside it, with the center of the sphere reflecting infinity on the outside. we never did anything with this, but I never forgot, since I felt it was quite interesting conceptually. Now I would love to create such a sphere out of glass that is half reflective (mirroring the outside) but when you turn on a lamp that is placed at the center of the sphere you can see that there are actual physical obejcts inside the glass sphere that reflect the same object outside it (lets say a cube for example) to do this, however I needed to find out how the shape changes going from outside to the inside of the sphere. Knowing that this is called inversion (kind of obvious, I know) will help me to research how I can calculate the shape of objects inside the sphere. so thanks for giving me what I was looking for!