A plane domainGw, symmetric with respect to the originO, is extended by “sector reflections” to a symmetric domain Ğw. A “mapping function” [Wbreve](z) of Ğw(mapping the unit diskGzonto Ğw) is constructed in an elementary way in terms of a mapping functionw(z) ofGwusing essentially the reflection principle. In the case of polygonal domains considered here, the results can be interpreted as relations between Schwarz-Christoffel integrals. This method applies to most domains considered in [2]. where only the ratio of conformal radiiRo(Ğw)/Ro(Gw) was determined. The study of the mapping functions themselves was suggested by Max Schiffer.