The monolayer morphologies of 1-monopalmitoyl-rac-glycerol at the air-water interface are studied at the microscopic level using Brewster angle microscopy (BAM). BAM images are recorded simultaneously with the pi-A isotherms to obtain information on the two-dimensional phase behavior. Condensed-phase domains of 1-monoglycerides exhibit a 7-fold substructure, which is analyzed according to a geometric model. The arrangement of regions of different azimuthal chain orientation affects the molecular orientation at the domain boundary. Therefore, If the line tension is anisotropic, the inner segment structure of a domain influences the outer domain shape. Restructuring processes induced by compression to high surface pressures cause zigzag segment boundary lines and 6-fold domains.