for Hermann–Mauguin symbols of corresponding space groups, where secondary directions are directions of symmetry elements along unit cell translations b and c, while the tertiary directions correspond to the direction between unit cell translations b and c. For example, symbols Pm2 and P2m denote two different space groups. This also applies to symbols of space groups with odd-order axes 3 and . The perpendicular symmetry elements can go along unit cell translations b and c or between them. Space groups P321 and P312 are examples of the former and the latter cases, respectively. The symbol of point group may be confusing; the corresponding Schoenflies symbol is D3d, which means that the group consists of 3-fold axis, three perpendicular 2-fold axes, and 3 vertical diagonal planes passing between these 2-fold axes, so it seems that the group can be denoted as 32m or 3m2. However, one should remember that, unlike Schoenflies notation, the direction of a plane in a Hermann–Mauguin symbol is defined as the direction perpendicular to the plane, and in the D3d group all mirror planes are perpendicular to 2-fold axes, so they should be written in the same position as . Second, these complexes generate an inversion center, which combining with the 3-fold rotation axis generates a rotoinversion axis. Groups with n = ∞ are called limit groups or Curie groups. Groups with several higher-order axes These are the crystallographic groups of a cubic crystal system: 23, 432, , 3m, and . All of them contain four diagonal 3-fold axes. These axes are arranged as 3-fold axes in a cube, directed along its four space diagonals (the cube has symmetry). These symbols are constructed the following way: First position — symmetrically equivalent directions of the coordinate axes x, y, and z. They are equivalent due to the presence of diagonal 3-fold axes. Second position — diagonal 3 or axes. Third position — diagonal directions between any two of the three coordinate axes x, y, and z. These can be 2, m, or . All Hermann–Mauguin symbols presented above are called full symbols. For many groups they can be simplified by omitting n-fold rotation axes in positions. This can be done if the rotation axis can be unambiguously obtained from the combination of symmetry elements presented in the symbol. For example, the short symbol for is mmm, for is mm, and for is mm. In groups containing one higher-order