<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">C. Chieh</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Geometric units in hexagonal and rhombohedral space groups</style></title><secondary-title><style face="normal" font="default" size="100%">Acta Cryst. (1984). A40, 567-571</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">1984</style></year></dates><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">Hexagonal space groups,&amp;nbsp;&lt;i&gt;i.e.&lt;/i&gt;&amp;nbsp;those with an&amp;nbsp;&lt;i&gt;hP&lt;/i&gt;&amp;nbsp;lattice, are classified from the geometric-unit viewpoint by considering hexagonal crystal structures as combinations and permutations of some basic hexagonal prisms. Geometric units are the Dirichlet domains of the Wyckoff positions with the highest point-group symmetry in the space group. In this classification, there are six types of hexagonal space groups. Type&amp;nbsp;&lt;i&gt;h&lt;/i&gt;1 consists of two independent geometric units of the same symmetry per crystallographic cell; in type&amp;nbsp;&lt;i&gt;h&lt;/i&gt;2, the two units are identical, but differently oriented. Type&amp;nbsp;&lt;i&gt;h&lt;/i&gt;3 has six independent geometric units, again of the same point-group symmetry, but the six units can be made up of three pairs, each consisting of two identical units, thus giving rise to type&amp;nbsp;&lt;i&gt;h&lt;/i&gt;4. There are subclasses in types&amp;nbsp;&lt;i&gt;h&lt;/i&gt;l and&amp;nbsp;&lt;i&gt;h&lt;/i&gt;3. Centers of geometric units in&amp;nbsp;&lt;i&gt;h&lt;/i&gt;l(&lt;i&gt;a&lt;/i&gt;) and&amp;nbsp;&lt;i&gt;h&lt;/i&gt;3(&lt;i&gt;a&lt;/i&gt;) are uniquely defined by intersections of point-group symmetry elements, whereas those in&amp;nbsp;&lt;i&gt;h&lt;/i&gt;1(&lt;i&gt;b&lt;/i&gt;) and&amp;nbsp;&lt;i&gt;h&lt;/i&gt;3(&lt;i&gt;b&lt;/i&gt;) are not because the space groups in these subtypes are hemimorphic. Therefore, the two units along the polar axis may be combined as one. Type&amp;nbsp;&lt;i&gt;h&lt;/i&gt;5 consists of three units, each turned 120° from its neighbors owing to the screw axis 31, 32, 62 and 64. Similarly, type&amp;nbsp;&lt;i&gt;h&lt;/i&gt;6 has six units due to screw axes 61 and 65, and adjacent units are 60° apart. Rhombohedral space groups show two types of patterns: type&amp;nbsp;&lt;i&gt;r&lt;/i&gt;1 has two independent, and type&amp;nbsp;&lt;i&gt;r&lt;/i&gt;2 two identical, units. The h.c.p. and related structures are used to demonstrate the application of geometric units to crystal-structure descriptions.</style></abstract></record></records></xml>