The exaggerated angularity of the broad, flat-bottomed base of the young Apatesia helianthoides flower is brought about by the shapes of its (unequal) sepals. The sepal lobes, separate from before their upturn, overlap at the base and narrow sharply into shallow, external keeled parts, until the surfaces flatten into the rounded, out-curving tips.
The young petals, sporting pale salmon to dull cerise among other nuances, here just exceed the sepals in height. This is not always the case.
The lowest parts of some sepal lobes in picture show signs of the membranous margins they sometimes possess (Le Roux, et al, 2005; Leistner, (Ed.), 2000; Eliovson, 1990; Herre, 1971; iNaturalist).