Casimir energy inside a cavity with triangular cross section

For a certain class of triangles (with angles proportional to pi/N, Ngreater than or equal to3) we formulate an image method by making use of the group G(N) generated by reflections with respect to the three lines which form the triangle under consideration. We formulate the regularization procedure by classification of subgroups of G(N) and corresponding fixed points in the triangle. We then also calculate Casimir energy for a cavity of infinite height with triangular cross section for scalar massless fields. More detailed calculation is given for odd N. (C) 2004 American Institute of Physics.