NavList:

Hi George

You requested that I sketch an octant for myself, showing the paths.

Linked, find just that image. To be clear about the sketch, here are some
considerations

1) I made no attempt to optimize for index mirror size. Clearly, I could do so
2) The angles were arbitrarily selected, again, no optimization
3) The horizon, foresight view to horizon and backsight view to horizon are
all parallel
4) The view to the zenith for the foresight and backsight paths are parallel.
5) All of the normals are shown, as well as, angles. (this is a sketch, don't expect arc-second accuracy).

Conclusion #1: The arrangement I have sketched can be made to work by optimizing angles for index mirror size.
Conclusion #2: The paths are indeed parallel.
Conclusion #3: I am not "wrong", with all due respect to your opinion.

This may be an unusual circumstance in which multiple folks are right without actually agreeing on the details! How? There are many arrangements which can
be made to work. There is no one definition of an octant and how the mirrors are arranged.

I believe that the main difference is that you required the beam from the object to strike the index mirror in the same spot, and with a differing angle to each horizon mirror. This is not a requirement with a planar mirror, as can be seen in my sketch.

Best Regards
Brad

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