Spot diagram borders are always caustic curves and/or marginal rays III: segmented mirror in hexagons and trapezoids

For annular (circular and elliptical) and hexagonal exit pupils with any optical path differences (described by Zernike Polynomials), it was proven [ Appl. Opt. 61 , 1876 ( 2022 ) APOPAI 0003-6935 10.1364/AO.449270 ; Appl. Opt. 61 , C20 ( 2022 ) APOPAI 0003-6935 10.1364/AO.435850 ] that the border of any spot diagram is composed of the caustic surface and/or marginal rays. In this paper, the previous results are extended to segmented (by hexagons or trapezoids) exit pupils. Examples with exact spherical, coma, and astigmatism aberrations are included, while a mathematical demonstration is also included.