Hexagonal Crystal System: Symmetry Elements and Classes

Hexagonal Crystal System: Symmetry Elements and Classes

Introduction

• The Hexagonal Crystal System is one of the most important crystal systems in crystallography. It is distinguished by its characteristic six-sided symmetry and the presence of a six-fold rotational axis. Many minerals crystallize in this system and develop beautiful hexagonal prisms and pyramids. Because of its unique symmetry and crystal forms, the hexagonal system occupies a special place in mineralogy and crystallographic studies.

Characteristics of the Hexagonal Crystal System

• The hexagonal system contains four crystallographic axes. Three horizontal axes, known as a₁, a₂, and a₃, are equal in length and lie in the same plane. These axes intersect each other at angles of 120°. The fourth axis, known as the c-axis, is vertical and differs in length from the horizontal axes. This arrangement produces the characteristic six-sided geometry of hexagonal crystals.

Crystallographic Axes

• The three horizontal axes are equally spaced and form the foundation of hexagonal symmetry. The vertical axis passes through the center of the crystal and serves as the principal symmetry axis. The relationship between these axes determines the shape and symmetry of all hexagonal crystal forms.

Symmetry Elements of the Hexagonal System

Six-Fold Axis of Symmetry

• The most important symmetry element of the hexagonal system is the six-fold rotational axis. When a crystal is rotated through 60° around this axis, it appears unchanged. This six-fold axis is the defining feature of the hexagonal crystal system and is responsible for its characteristic crystal shapes.

Planes of Symmetry

• Many hexagonal crystals possess mirror planes that divide the crystal into equal mirror-image halves. These planes may occur vertically or horizontally depending on the crystal class. The number of mirror planes increases with the symmetry of the crystal.

Centre of Symmetry

• Certain crystal classes within the hexagonal system contain a centre of symmetry. This symmetry element ensures that crystal features are arranged equally around the center of the crystal.

Secondary Axes of Symmetry

• In addition to the principal six-fold axis, some hexagonal classes contain several two-fold rotational axes. These additional axes contribute to the high symmetry of the crystal and influence its external form.

Crystal Classes of the Hexagonal System

Hexagonal Pyramidal Class (6)

• This class contains a single six-fold rotational axis and no mirror planes. It represents one of the simpler symmetry classes of the hexagonal system. Crystals belonging to this class commonly develop pyramid-shaped forms.

Trigonal Dipyramidal Class (−6)

• The Trigonal Dipyramidal Class contains a six-fold rotoinversion axis. This symmetry element combines rotation and inversion and produces unique crystal forms not seen in ordinary pyramidal crystals.

Hexagonal Dipyramidal Class (6/m)

• This class contains a six-fold rotational axis together with a horizontal mirror plane. The additional symmetry element produces more balanced and symmetrical crystal forms.

Hexagonal Trapezohedral Class (622)

• The Hexagonal Trapezohedral Class possesses one six-fold axis and several two-fold axes. The combination of these symmetry elements creates highly symmetrical trapezohedral crystal forms.

Dihexagonal Pyramidal Class (6mm)

• This class contains a six-fold axis and multiple vertical mirror planes. The presence of these mirror planes increases the symmetry and produces well-developed pyramidal crystal forms.

Ditrigonal Dipyramidal Class (−6m2)

• The Ditrigonal Dipyramidal Class possesses a combination of rotoinversion axes and mirror planes. This results in complex crystal forms with distinctive symmetry characteristics.

Dihexagonal Dipyramidal Class (6/mmm)

• The Dihexagonal Dipyramidal Class is the normal class of the hexagonal crystal system. It possesses the maximum number of symmetry elements possible within the system. These include a six-fold rotational axis, several two-fold axes, numerous mirror planes, and a centre of symmetry.

Common Crystal Forms in the Hexagonal System

Hexagonal Prism

• The hexagonal prism is the most characteristic crystal form of this system. It consists of six rectangular faces arranged around the vertical axis and often develops as elongated crystals.

Hexagonal Pyramid

• The hexagonal pyramid consists of six triangular faces that meet at a common point. This form commonly occurs at the ends of hexagonal prisms.

Hexagonal Dipyramid

• The hexagonal dipyramid is formed when two pyramids are joined base to base. It is one of the most symmetrical forms found in the hexagonal system.

Minerals Belonging to the Hexagonal System

• Several important minerals crystallize in the hexagonal system and display characteristic six-sided crystal forms.
• Quartz is one of the most common minerals of the hexagonal system and frequently develops well-formed hexagonal prisms with pyramidal terminations.
• Beryl, including emerald and aquamarine varieties, often occurs as long hexagonal crystals.
• Apatite commonly develops hexagonal prisms and is widely distributed in igneous and sedimentary rocks.
• Graphite and Nepheline are also important minerals that belong to the hexagonal crystal system.

Importance of the Hexagonal System

• The Hexagonal Crystal System is important because it contains many economically and scientifically significant minerals. Its distinctive six-fold symmetry makes crystal identification easier and helps students understand advanced concepts of crystal symmetry. The study of hexagonal symmetry, crystal classes, and crystal forms provides valuable knowledge for mineral identification, crystallography, geology, and materials science.