axis, this higher-order axis cannot be omitted. For example, symbols and can be simplified to 4/mmm (or mm) and 6/mmm (or mm), but not to mmm; the short symbol for is m. The full and short symbols for all 32 crystallographic point groups are given in crystallographic point groups page. Besides five cubic groups, there are two more non-crystallographic icosahedral groups (I and Ih in Schoenflies notation) and two limit groups (K and Kh in Schoenflies notation). The Hermann–Mauguin symbols were not designed for non-crystallographic groups, so their symbols are rather nominal and based on similarity to symbols of the crystallographic groups of a cubic crystal system. Group I can be denoted as 235, 25, 532, 53. The possible short symbols for Ih are m, m, mm, m. The possible symbols for limit group K are ∞∞ or 2∞, and for Kh are ∞ or m or ∞∞m. Plane groups Plane groups can be depicted using the Hermann–Mauguin system. The first letter is either lowercase p or c to represent primitive or centered unit cells. The next number is the rotational symmetry, as given above. The presence of mirror planes are denoted m, while glide reflections are only denoted g. Screw axes do not exist in two dimension, they required 3D space. Space groups The symbol of a space group is defined by combining the uppercase letter describing the lattice type with symbols specifying the symmetry elements. The symmetry elements are ordered the same way as in the symbol of corresponding point group (group that is obtained if one removes all translational components from the space group). The symbols for symmetry elements are more diverse, because in addition to rotations axes and mirror planes, space group may contain more complex symmetry elements—screw axes (combination of rotation and translation) and glide planes (combination of mirror reflection and translation). As a result, many different space groups can correspond to the same point group. For example, choosing different lattice types and glide planes one can generate 28 different space groups from point group mmm, e.g. Pmmm, Pnnn, Pccm, Pban, Cmcm, Ibam, Fmmm, Fddd. Lattice types These are the Bravais lattice types in three dimensions: P — Primitive I — Body centered (from the German "Innenzentriert") F — Face centered (from the German "Flächenzentriert") A — Base centered on A faces only B — Base centered on B faces only C — Base centered