We have studied the cathodoluminescence of AlxGa1-xAs/GaAs multilayers grown on ridge-type triangles by molecular beam epitaxy. The compositional variation of Al, as well as the distribution of impurity and/or defect, was revealed by variations in the cathodoluminescence spectra and images. The Al composition in an AlxGa1-xAs layer was highest in the (111)A facet and decreased in the order (100), (411)A, (111)-delta and (110) facets. On the other hand, the carbon concentration was highest in the (411)A facet and decreased in the order (111)A, (111)-delta, (100) and (110) facets. It should be noted that the (111)-delta facet has a significant effect on the redistribution of Al. Although our ridge-type triangles are rather large for the quantum structures, these data have elucidated the self-organization mechanism of the AlxGa1-xAs/GaAs system and have yielded information on the design of quantum structures. We conclude that cathodoluminescence observation is a powerful tool for studying the compositional variation or band structure of three-dimensional microscale or nanoscale construction.