A "periodic table" for supersymmetric M-theory compactifications

We develop a systematic method for classifying supersymmetric orbifold compactifications of M-theory. By restricting our attention to Abelian orbifolds with low order, in the special cases where elements do not include coordinate shifts, we construct a "periodic table" of such compactifications, organized according to the orbifolding group (order less than or equal to12) and dimension (up to 7). An intriguing connection between supersymmetric orbifolds and G(2) structures is explored. (C) 2003 American Institute of Physics.