An approximate expression for multiple-edge diffraction of sound around a polygonal cylinder is derived based on Pierce's approximate solution for sound diffraction field around a hexagonal cylinder, which is also obtained experimentally through a sound visualization method using three color-light-emitting diodes. The hexagonal cylinder model used in this experiment has a circular aperture on its side surface and a speaker inside. A circular cylinder model is also used. It is, moreover, investigated whether the diffraction field around a cimcular cylinder may be estimated using the hexagonal cylinder inscribed in it or not. It is shown that the computed results agree well the visualized ones and that the diffraction field around a circular cylinder can be approximately estimated using the hexagonal cylinder inscribed in it.