If you look into the corner of the intersection between two mirrors at right angles, at 60 degrees, 45 degrees etc you get a series of confusingly-behaved reflections. Think about them and explain.

If you have a bit of cash and suitable tools, explore and explain what you see if you let three mirrors meet at a corner, in particular, two can be normal rectangular mirrirs, but you can do a bit of geometry and cut triangles at various angles to make corner cubes, sixty-degree-corners and so on. (Trickier than it sounds!)

But now, something that I would love to see would be cones of good glass or optical grades of plastic that one could look into from below. I have ideas about what they would show, but has anyone seen such things in real life?

Or is there a good bit of ray-tracing freeware that would help?