Holohedral class

Molecules of the ineso form of 2,3 dibromobutane Br(CH3)HC— CH(CH3)Br have a centre of symmetry (I) as their only element of symmetry j (Stevenson and Schomaker, 1939), resembling in this respect crystals belonging to the holohedral class of the triclinic system. It is worth noting that the d and l isomers are not asymmetric they possess one twofold axis.j... 

Within each of the six crystal systems, there arc specific crystal classes. Each class displays distinctive symmetry elements. There are 32 possible classes distributed among the six crystal systems. One of the crystal classes within each system possesses all of the symmetry elements that re characteristics of its space lattice cell. These are ealled the holohedral class of that system. Other classes within each system possess somewhat fewer symmetry elements and are called tncmhedral classes. 

Each crystal system contains several classes that exhibit only a partial symmetry for instance, only one-half or one-quarter of the maximum number of faces permitted by the symmetry may have been developed. The holohedral class is that which has the maximum number of similar faces, i.e. possesses the highest degree of symmetry. In the hemihedral class only half this number of faces have been developed, and in the tetrahedral class only one-quarter have been developed. For example, the regular tetrahedron (4 faces) is the hemihedral form of the holohedral octahedron (8 faces) and the wedge-shaped sphenoid is the hemihedral form of the tetragonal bipyramid Figure 1.9). 

The general simple form of the new class will be 1/8 of the number of the simple general faces of holohedric class. 

The three merihedric classes are exemplified in Figure 2.50. In fact, all the merihedric classes can be considered as hemihedric of a holohedric class, or of other hemihedric or even of a tetartohedric. 

The benzene molecule (Pauling and Brockway, 1934) has a sixfold axis of rotation, together with all the additional symmetry elements possessed by a crystal belonging to the holohedral hexagonal class 6/mmm. 

Sodium nitrite, NaN02, forms orthorhombic crystals of the shape of Fig. 179. This shape has holohedral symmetry mmm the internal symmetry might, however, be lower than this (see p. 269), and therefore atomic arrangements in all three classes of the orthorhombic system (mmm, 222, and mm2) may be considered. 

Class No. 5 holohedral- prismatic (Baumhauer, Pogg. Annalen, 1873, 150, 619 confirmed by Tutton, loc. cif.). 

Monoclinic crystal system the holohedric group Gift, and those sub-groups which do not belong to class 1 (one specific direction is defined) Czh Cs, Cg... 

Table 2.14. Holohedral and merohedral classification of the crystal classes...

A class of symmetry is called holohedric, when its general simple form has the maximum number of possible faces in this system in cause. The symmetry classes with a lower number of symmetry elements are called as merihedric. 

---