Abstract
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 up to 12) and dimension (up to 7). An intriguing connection between supersymmetric orbifolds and G2-structures is explored.
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