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The synchronized self-motion of two camphor boats on polygonal water chambers was investigated. The two boats synchronously moved depending on the number of corners in the polygon by changing the distance between the two boats through the corners. We regard the self-motion of a camphor boat as an oscillator; i.e., one cycle on the polygonal chamber corresponds to 2pi. Phase-locked synchronization at a phase difference of 2pi/3, which corresponds to the length of one side of the chamber, was observed with a triangular chamber. Two types of synchronized motion at phase differences of pi/2 and pi, which correspond to the length of one and two sides of the chamber, respectively, were observed with a square chamber. These characteristic features of synchronized self-motion were qualitatively reproduced by a numerical calculation that regarded the surface tension as the driving force and the number of corners in the chamber as a velocity-regulating mechanism. We believe that the present system may be a simple model of synchronization which depends on the geometry of the system.