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 the trigonal crystal system.
The space groups associated with the hexagonal crystal system are
\[
\begin{array}{lll}
168. ~ \text{P6} & 169. ~ \text{P6$_{1}$} & 170. ~ \text{P6$_{5}$} \\
171. ~ \text{P6$_{2}$} & 172. ~ \text{P6$_{4}$} & 173. ~ \text{P6$_{3}$} \\
174. ~ \text{P$\overline{6}$} & 175. ~ \text{P6/m} & 176. ~ \text{P6$_{3}$/m} \\
177. ~ \text{P622} & 178. ~ \text{P6$_{1}$22} & 179. ~ \text{P6$_{5}$22} \\
180. ~ \text{P6$_{2}$22} & 181. ~ \text{P6$_{4}$22} & 182. ~ \text{P6$_{3}$22} \\
183. ~ \text{P6mm} & 184. ~ \text{P6cc} & 185. ~ \text{P6$_{3}$cm} \\
186. ~ \text{P6$_{3}$mc} & 187. ~ \text{P$\overline{6}$m2} & 188. ~ \text{P$\overline{6}$c2} \\
189. ~ \text{P$\overline{6}$2m} & 190. ~ \text{P$\overline{6}$2c} & 191. ~ \text{P6/mmm} \\
192. ~ \text{P6/mcc} & 193. ~ \text{P6$_{3}$/mcm} & 194. ~ \text{P6$_{3}$/mmc} \\
\end{array}
\]