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3. Partial symmetry elements

Element sets of fourfold and sixfold rotation and screw rotation axes have subsets which fully satisfy the specifications in Table 2, last column. However, they do not contain all symmetry operations with the given axis as geometric element. In order to distinguish such incomplete symmetry elements from the regular ones, it is recommended that they be referred to as `partial symmetry elements'; they will be designated by EP instead of E. Examples: EP2 in E4; EP2₁ and EP3 in E6₃; EP2 and EP3₂ in E6₂.

The partial elements should not be confused with the regular symmetry elements defined by the powers of a rotoinversion: the square and cube of $\bar{6}^1$(defining an E3 and an Em) and of $\bar{3}^1$ (defining an E3 and an $E\bar{1}$), and the square $\bar{4}^2$ which defines an E2. The symmetry elements so defined are regular and by no means partial, provided that the corresponding element set is not a subset of any other element set (as happens for $\bar{4}^2$ in the second example below).

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