Phase information on wave scattering is not unique and greatly depends on a choice of the origin of coordinates in the measurement system. The present paper argues that the center of scattering for polygonal cylinders should not be a geometrical center of the obstacle such as a center of gravity but be a position that acts as a balance to the electrostatic field effects from edge points. The position is exactly determined in terms of edge positions, edge parameters and lengths of side of polygons. A few examples are given to illustrate a difference from the center of geometry.