The crystallographic restriction in higher dimensions

The crystallographic restriction in dimensions two and three is generalized to arbitrary dimensions. It is shown that m can occur as the order of an element of the point group of an n-dimensional space group if and only if Φ(m) ≤ n where Φ is an additive version of Euler's totient function. A table of these allowable orders in dimensions ≤ 23 is provided.