HOLOSYMMETRIC CLASS (Holohedral; Ditrigonal-scalenohedral.) In this class, which presents the corn monents type of symmetry of the hexa gonal system, the triad axis is associated with three similar planes of symmetry in clined to one another at 6o° and intersect ing in the triad axis ; there are also three similar dyad axes, each perpendicular to a plane of symmetry, and a centre of symmetry. The seven simple forms are : Rhombohedron (figs. 66 and 67), consisting of six rhomb shaped faces with the edges all of equal lengths: the faces are perpendicular to the planes of symmetry. There are two sets of rhombohedra, distinguished respectively as direct and inverse; those of one set (fig. 66) are brought into the orientation of the other set (fig. 67) by a rotation of 6o° or 18o° about the pal axis. For the fundamental dron, parallel to the edges of which are the crystallographic axes of reference, the dices are { Ioo } . Other rhombohedra may have the indices { 2 I I 1, WO, {IIo, 1227), { 1 I i } , etc., or in general { likk . (Compare fig. 72; for figures of other rhombohedra see CALCITE.) Scalenohedron (fig. 68), bounded by twelve scalene triangles, and with the general indices { likl } . The zigzag lateral edges coin cide with the similar edges of a rhombohedron, as shown in fig. 69; if the indices of the inscribed rhombohedron be { Ioo } , the indices of the scalenohedron represented in the fig ure are { 2oi } . The scalenohedron { 2oi} is a characteristic form of calcite, which for this reason is sometimes called "dog-tooth spar." The angles over the three edges of a face of a scalenohedron are all different; the angles over three alternate polar edges are more obtuse than over the other three polar edges. Like the two sets of rhombo hedra, there are also direct and inverse scalenohedra, which may be similar in form and angles, but different in orienta tion and indices.
Hexagonal bipyramid (fig. 7o), bounded by twelve isosceles tri angles each of which are equally inclined to two planes of sym metry. The indices are { no } , { 41 a } , etc., or in general { hkl } where h-2k+l=o.
Hexagonal prism of the first order { 2 I I 1, consisting of six faces parallel to the principal axis and perpendicular to the planes of symmetry; the angles between (the normals to) the faces are 6o°.
Hexagonal prism of the second order { Ioi } , consisting of six faces parallel to the principal axis and parallel to the planes of symmetry. The faces of this prism are inclined to 3o° to those of the last prism.
Dihexagonal prism, consisting of twelve faces parallel to the principal axis and inclined to the planes of symmetry. There are two sets of angles between the faces. The indices are { 3 2 I } , . . . { hkl } where Basal pinacoid fir I } consist ing of a pair of parallel faces per pendicular to the principal axis.
Fig. 71 shows a combination of a hexagonal prism (in) with the basal pinacoid (c) For figures of other combinations see CALCITE and CORUNDUM. The relation be tween rhombohedral forms and their indices are best studied with the aid of a stereographic projection (fig. 72) ; in this figure the thicker lines are the projections of the three planes of symmetry, and on these lie the poles of the rhombohedra (six of which are indicated).
Numerous substances, both natural and artificial, crystallize in this class; for example, calcite, chaly bite, smithsonite, corundum (ruby and sapphire), haematite, chabazite; the ele ments arsenic, antimony, bismuth, selen ium, tellurium and perhaps graphite ; also ice, sodium nitrate, thymol, etc.