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Dan, thanks for taking the time on this entry.

The basic idea is that the Nexus squares/cells are the same on each side.
When you go to the 7th row, you are effectively on both planes at the same
time, however, bending space dimensions mean that they are different
cells, but it is up to the player to decide which of the two cells the
piece is in, or has moved to. That is, moving from 6 to 7 you can choose
to be in T17 or F67.

This is confusing, and looking again at the pictures that I created
representing the moves of the pieces, I realize that there are some
errors. For example, the knight when moving from the flipside to the
topside, didn't take the flipping of the board into account. The picture
shows the topside final position of the knight incorrectly, they should be
flipped with respect to the 11 o'clock, 5 o'clock axis. So the final
possible positions are actually still on dark spaces, which is a change
from conventional chess where the knight always changes color.

Regarding the board diagrams and pictures, using your notation, the
flipside of T21 is F51, and F12 is on the other side of T62. The 11
o'clock, 5 o'clock diagonal is the axis of rotation for thinking about the
flipside.