Crystal faces are found in different forms. A ”form” consists of a group of crystal faces all of which have the same relation to the elements of symmetry. The number of faces in a form is determined by the symmetry of the crystal class. Miller indices may be used to represent forms and they are then enclosed in brackets.
Closed and Open Forms:
A closed-form is that whose faces enclose spaces and can exist alone. The cube and the octahedron in the cubic system are both closed forms. Faces of an ”open form” do not enclose space. In a crystal, an open form always occurs in combination with other forms. An example of an open form is a prism.
Holohedral and Hemihedral Forms:
In a crystal system, each form of the normal class is called the ”holohedral form”. This form contains all the possible faces that have a similar relation to the elements of symmetry. However, in the lower symmetry classes, there are some forms, which contain half the number of faces found in the corresponding holohedral form. Such a form is called the ”hemihedral form”. It may be noted that to account for all the faces of the holohedral form, two similar hemihedral forms exist. They are called ”positive” and ”negative” respectively. Form example, in the cubic system, the tetrahedron is the hemihedral form of an octahedron. The positive and negative tetrahedron is shown in the following figure.
In the lower symmetry classes of some systems, there are some crystal forms in which faces occur only on one end of the vertical crystallographic axis. Such forms are called ”hemimorphic forms”. Obvious crystals with hemimorphic forms, such as tourmaline, have no center of symmetry.
Crystals, which do not possess a plane and center of symmetry, contain a form that occurs in two positions and which are mirror images of each other. These two positions are related in the same way as right and left hand and are not interchangeable. Such a form is called ”enantiomorphous form”. Tourmaline is a mineral that shows a hemimorphic form, while the quartz mineral shows an enantiomorphous form.