Oh, you are right. My 3d example is bad indeed. Thanks for pointing it out.
I think my mistake from the very beginning was to frame „reflection“ as happening around a vector instead of around a plane. I did this because I thought of it to be easier to vidualize. The I carried it on into 3d but as you say it does not generalize.
Had I started with doing reflections across planes I think it might generalize correctly across dimensions.
I have to admit this kind of mistake might completely undermine the correctness and usefulness of the visualization. I will rework this.
Glad you noticed it.
I think my mistake from the very beginning was to frame „reflection“ as happening around a vector instead of around a plane. I did this because I thought of it to be easier to vidualize. The I carried it on into 3d but as you say it does not generalize.
Had I started with doing reflections across planes I think it might generalize correctly across dimensions.
I have to admit this kind of mistake might completely undermine the correctness and usefulness of the visualization. I will rework this. Glad you noticed it.