Regularized Green's function and group of reflections in a cavity with triangular cross section

For a certain class of triangles (with angles proportional to pi/N, N >= 3) we formulate the image method by making use of the group G(N) generated by reflections with respect to three lines which form the triangle under consideration. A regularized Green's function which is employed in Casimir energy calculations) is obtained by classification Of Subgroups of G(N) and corresponding fixed points in (he triangle. (c) 2005 Pleiades Publishing, Inc.