The Hexagonal Crystal System

The hexagonal crystal system has a six-fold rotation axis. There is only one Bravais lattice in this system, the hexagonal Bravais lattice given by the same lattice vectors as the hexagonal lattice vectors, described in trigonal crystal system. The space groups associated with the hexagonal crystal system and lattice are \begin{array}{lll} 168. ~ \mbox{P6} & 169. ~ \mbox{P6$_{1}$} & 170. ~ \mbox{P6$_{5}$} \\ 171. ~ \mbox{P6$_{2}$} & 172. ~ \mbox{P6$_{4}$} & 173. ~ \mbox{P6$_{3}$} \\ 174. ~ \mbox{P$\overline{6}$} & 175. ~ \mbox{P6/m} & 176. ~ \mbox{P6$_{3}$/m} \\ 177. ~ \mbox{P622} & 178. ~ \mbox{P6$_{1}$22} & 179. ~ \mbox{P6$_{5}$22} \\ 180. ~ \mbox{P6$_{2}$22} & 181. ~ \mbox{P6$_{4}$22} & 182. ~ \mbox{P6$_{3}$22} \\ 183. ~ \mbox{P6mm} & 184. ~ \mbox{P6cc} & 185. ~ \mbox{P6$_{3}$cm} \\ 186. ~ \mbox{P6$_{3}$mc} & 187. ~ \mbox{P$\overline{6}$m2} & 188. ~ \mbox{P$\overline{6}$c2} \\ 189. ~ \mbox{P$\overline{6}$2m} & 190. ~ \mbox{P$\overline{6}$2c} & 191. ~ \mbox{P6/mmm} \\ 192. ~ \mbox{P6/mcc} & 193. ~ \mbox{P6$_{3}$/mcm} & 194. ~ \mbox{P6$_{3}$/mmc} \\ \end{array}