u/BadJimo

Four tangent (kissing) spheres.

https://www.desmos.com/3d/0fw8xdiedu

I started with a regular tetrahedron with spheres of the same size at the vertices and then applied a 3D Möbius transformation known as Spherical Inversion.

​A spherical inversion turns 3D space inside-out through a "lens" (a sphere of inversion). Things close to the lens get blown up and pushed far away, while things far away get shrunk and pulled inside.

​An important property of this transformation is that it preserves tangency. If two spheres kiss before the inversion, they will kiss after the inversion.

To change the sizes of the sphere you move the "Center of Inversion" (using the sliders o,p,q).

I realized a corner cube reflector only requires a single line to define the ray of light.

https://www.desmos.com/3d/3vb2nni5j4