If you are programming for a vertical machine
then the BACK & BOTTOM views are incorrect--- they are drafting views & are not capable of being achieved on a machine with the 4th axis around X.
- they should be created as seen by the operator ( or by the tool looking in the Z- direction ) as it rotates around the axis.
Your WCS for all operations should be TOP. ( this is your actual setup, & angles all relate back to this view )
your T/C planes you should use :-
- TOP view gives the A0. output
- FRONT view would generate the A-90.
- NEW BOTTOM ( rotated around Z by 180° ) gives A180. or A-180. ( depends on what direction you come from )
- NEW BACK ( rotated around Z by 180° ) gives you the A90. ( or A-270. )
- WCS is TOP for all ops, working face is FRONT ( gives B0. outputs )
RIGHT(B90.), BACK(B180.) & LEFT(B270.) all fall in correctly.
TOP & BOTTOM views are NOT usable on a 4-axis horizontal