It is relatively easy to fit equal area maps into regular N sided polygons. One computer program can do them all, starting, as in the previous illustration, with N=3. Beyond about N=20 it is not very interesting because the maps all converge to Lambert’s (1772) azimuthal equal area projection with a circular boundary. W. Tobler 1972, “Lambert’s Notes on Maps”, Introduction and Translation of his “Beitraege, 1772”, Ann Arbor, 125 pages.
The next map fits into a pentagon