Forms may be classified in three ways

I. (i) Simple form:

When a crystal is made up of all like faces such as cube, octahedron, etc.

(ii) Combination form:

When a crystal is made up of two or more simple forms, such as when it consists of basal pinacoid and prism faces, each of which in itself is a simple form.

II. (i) Open form:

These forms whose faces cannot enclose space all by themselves, as they do not have adequate number faces to do so and as a result occur only in combination with other forms, such as pinacoids and prisms.

(ii) Closed form:

It is an assemblage of faces, which can enclose a volume of space.

III. (i) General form:

It is one in which the indices are unrestricted in magnitude.

(ii) Special form:

Here only one possible set of values exist for the indices (hkl), e.g., only one octahedron (III) is possible in the cubic.

(iii) Restricted form:

When the forms are neither special nor general-part of their index is variable and part fixed, e.g., in a prism (hkl), ‘l’ must always be zero and in trisoctahedra of the cubic system, ‘h’ must always equal ‘k’, this type of forms are called restricted forms.

Besides the above classification, forms have also been classified as

(a) Holohedral forms:

These forms exhibit the highest degree of symmetry possible in a system.

(b) Hemihedral forms:

These forms show half the number of faces required for the full symmetry of the system, e.g., tetrahedron is a hemihedral form of octahedron.

(c) Hemi-morphic forms:

These forms have dissimilar faces about the two ends an axis of symmetry. This axis is called the polar axis. Thus half of the faces of a holohedral form are grouped about one end of the axis and none at the other. Hemimcrphic forms lack centre of symmetry.

(d) Tetartohedral forms:

They show only a quarter of the number of faces of the corresponding holohedral form. These forms have neither plane nor centre of symmetry.

(e) Enantiomorphic forms:

These forms do not have either plane or centre of symmetry and occur in two positions which are mirror images of each other. They cannot be converted into each other by any rotation whatsoever.

Common Forms in Crystallography:

(i) Pedion:

It is represented by one face only.

(ii) Pinacoid:

It is an open form, consisting of two faces which cuts one crystallographic axis and remains parallel to the remaining axes.

(iii) Prism:

It is also an open form, consisting of four faces, each face of which essentially parallel the vertical axis and cuts one or more horizontal axes.

(iv) Pyramids:

It is a closed form having eight faces, each face of which cuts the vertical axis and cuts one or more horizontal axes, at equal or unequal distances.

(v) Domes:

It is an open form intermediate between a prism and a pyramid, whose faces cut the vertical axis and one of the horizontal axes. These are also known as ‘Horizontal prism’.

(vi) Diametral Prisms:

It is formed by the combination of three pinacoids which together enclose space. They occur only in the Orthorhombic, Monoclinic and Triclinic systems in which all the pinacoids occur.

Elements of Symmetry:

Crystals also show certain regularity of positions of facet, edges, corners, solid-angles etc. The geometric locus about which a group of repeating operations act is known as a symmetry element. Sometimes the repetition is with respect to a point, in which case it has ‘centre of symmetry’, sometimes it is with respect to a line, in which case, it has an ‘axis of symmetry’ and when the repetition is with respect to a plane, it is said to have a ‘plane of symmetry

1. Centre of symmetry:

The point within a crystal through which straight lines can be drawn so that on either side and at the same dis­tance from the centre similar faces, edges and solid angles are encoun­tered, is known as the centre of symmetry. In other words, a crystal is said to possess a centre of symmetry, when for each face, edge, corner etc., on one side of the crystal, there is a similar face, edge or corner, directly on the opposite side of the centre point.

2. Axis of symmetry:

It is an imaginary line about which if the crystal is allowed to rotate through an angle of 360°. Similar faces, edges and Solid angles will come to the space for more than once. If it comes twice, the axis is an axis of ‘two fold’ symmetry; if it occurs thrice, it is an axis of three-fold symmetry.

The maximum number of axis of symmetry is ’13’and it is found in Isometric system.

3. Plane of symmetry:

It is an imaginary plane which passes through the centre of the crystal and divides it into two parts, such; that one part is the mirror image of the other. These planes of symmetry may be diagonal, horizontal as well as vertical.

There are maximum nine planes of symmetry, which the normal class of isometric system.

Symmetry elements have a particular relationship with the internal atomic structure of the crystals. Accordingly, they form the basis for the classification of crystals into thirty-two symmetry classes.

It is quite significant to note that the normal classes of all the systems show maximum number of symmetry elements, but the other classes consisting of hemihedral, hemi-morphic, tetarohedral and enantiomorphic forms show minimum number of symmetry elements in comparison to the normal class which consists of the holohedral forms.

Pseudo-symmetry:

Crystals of certain species imitate the sym­metry of a class or a system higher or lower than to which they actually belong. It may be due to twinning, distortion or by imitation of interfacial angles.