The Hexagonal Crystal System

Four axes, sixfold symmetry, and some of the most important gem species on earth

Gemmological scienceView in dictionary · 1,290 words

The hexagonal crystal system is one of the seven fundamental crystal systems recognised in crystallography, defined by a unique axial arrangement that produces the characteristic sixfold rotational symmetry visible in many of its mineral members. Gem species crystallising in this system include beryl — the family encompassing emerald, aquamarine, morganite, and heliodor — as well as apatite, and, depending on the classification scheme used, corundum (ruby and sapphire). Understanding the hexagonal system is foundational to gemmology: it governs crystal habit, cleavage, optical behaviour, and the directional colour phenomena that make so many of these stones commercially and scientifically significant.

Axial Geometry

The hexagonal system is distinguished from all other crystal systems by its use of four crystallographic axes rather than three. Three of these axes — conventionally labelled a₁, a₂, and a₃ — are of equal length and lie in a single horizontal plane, intersecting one another at angles of 120°. The fourth axis, the c-axis, stands perpendicular to this plane and is of a different length, either longer or shorter than the a-axes depending on the mineral. This geometry is sometimes described using the Miller–Bravais four-index notation (hkil), which accommodates the three equivalent horizontal axes more elegantly than the standard three-index system used for other crystal systems.

The defining symmetry element is a single sixfold rotation axis (C₆) coinciding with the c-axis: rotating a crystal 60° about this axis brings it into an indistinguishable orientation. This sixfold axis distinguishes the hexagonal system proper from its close relative, the trigonal system (sometimes called the rhombohedral system), which possesses only a threefold rotation axis. The two systems share the same four-axis notation and are sometimes grouped together as a single hexagonal division, which is why corundum — strictly trigonal — is frequently discussed alongside hexagonal minerals in gemmological literature.

Crystal Habit

The geometry of the hexagonal system expresses itself directly in the external form of well-crystallised specimens. Two habits predominate among gem-quality material:

Prismatic habit: Elongated crystals with a hexagonal cross-section, bounded by six prism faces running parallel to the c-axis and terminated by flat or pyramidal ends. Beryl is the paradigmatic example — the long, barrel-like crystals of aquamarine from Minas Gerais or the stubby emerald prisms of Muzo are immediately recognisable expressions of this habit.
Tabular habit: Flattened crystals in which the c-axis is compressed relative to the a-axes, producing disc-like or plate-like forms. Certain apatite crystals, and many corundum specimens from metamorphic deposits, adopt this habit — the flat, hexagonal sapphire crystals recovered from the Mogok Stone Tract in Myanmar being a well-known instance.

Crystal habit has direct practical consequences for the lapidary: the orientation of the rough relative to the c-axis determines how colour, pleochroism, and optical phenomena will appear in the finished stone.

Optical Properties: Uniaxial Character

All minerals in the hexagonal system (and the trigonal system) are optically uniaxial. This means they possess a single optic axis — coinciding with the crystallographic c-axis — along which light travels without being split into two rays of different velocity. In every other direction, incident light is resolved into two polarised rays travelling at different speeds, a phenomenon called double refraction or birefringence.

Uniaxial minerals are characterised by two principal refractive indices:

n_o (the ordinary ray index), which is constant regardless of the direction of light propagation.
n_e (the extraordinary ray index), which varies with direction and reaches its maximum or minimum value when light travels perpendicular to the c-axis.

When n_e is greater than n_o, the mineral is termed optically positive; when n_e is less than n_o, it is optically negative. Beryl is optically negative (typical n_o ≈ 1.577–1.583, n_e ≈ 1.572–1.578), while apatite is also optically negative in most compositions. Corundum is optically negative as well (n_o ≈ 1.769–1.772, n_e ≈ 1.760–1.763). These refractive index ranges, measurable on a refractometer, are among the primary diagnostic tools used by gemmologists to identify members of this system.

Pleochroism

A direct consequence of uniaxial optics is dichroism — the display of two distinct colours or colour intensities when a crystal is viewed along different crystallographic directions. Because there is only one optic axis, uniaxial stones show two pleochroic colours rather than the three seen in biaxial (orthorhombic, monoclinic, or triclinic) minerals.

Pleochroism in hexagonal and trigonal gem species has significant practical implications:

In aquamarine, the c-axis direction typically shows a stronger, more saturated blue, while the direction perpendicular to it appears paler or greenish-blue. Cutters orient the table facet perpendicular to the c-axis to maximise the desirable blue colour in the face-up view.
In ruby, the ordinary ray (n_o) direction displays the richest red, while the extraordinary ray (n_e) direction tends toward orange-red. Cutters similarly orient the table to favour the ordinary ray colour.
In emerald, pleochroism is less commercially decisive but still measurable — one direction appearing a slightly more yellowish-green, the other a purer green.

Cleavage and Fracture

Cleavage in hexagonal minerals is governed by the symmetry of the system. Beryl exhibits imperfect basal cleavage perpendicular to the c-axis, which rarely poses a significant cutting problem but can be relevant when setting stones that may receive impact. Apatite has distinct cleavage in two directions. Corundum, by contrast, has no true cleavage — a property that, combined with its hardness of 9 on the Mohs scale, makes it exceptionally durable in wear. Instead, corundum exhibits parting along rhombohedral planes, a structural discontinuity that can occasionally be mistaken for cleavage but is mechanistically distinct.

Principal Gem Species

The gemmological importance of the hexagonal system is difficult to overstate. Its principal gem members include:

Beryl (Be₃Al₂Si₆O₁₈): The most commercially diverse hexagonal gem family, encompassing emerald (chromium- and vanadium-bearing green), aquamarine (iron-bearing blue), morganite (manganese-bearing pink-orange), heliodor (iron-bearing yellow), and goshenite (colourless). Beryl crystallises in the hexagonal system proper, space group P6/mcc.
Apatite (Ca₅(PO₄)₃(F,Cl,OH)): A phosphate mineral occurring in a wide range of colours — neon blue-green from Madagascar and Tanzania, yellow from Mexico, violet from Maine — and valued as a collector's gem. Its relatively low hardness (5 on the Mohs scale) limits its use in everyday jewellery.
Corundum (Al₂O₃): Strictly trigonal (space group R3̄c), but conventionally grouped with the hexagonal division in most gemmological curricula. Ruby and sapphire are the most commercially important members of this group, and their optical and physical properties are entirely consistent with the uniaxial, four-axis framework described above.

Relevance to Gemmological Testing

Recognition of the hexagonal system underlies several routine gemmological procedures. On the refractometer, uniaxial stones produce a characteristic shadow-edge reading in which one index remains stationary as the stone is rotated on the hemisphere while the other moves — a pattern distinct from the behaviour of biaxial stones. Under the polariscope, hexagonal and trigonal stones display the uniaxial interference figure: a dark cross (isogyres) surrounded by concentric coloured rings (isochromes) when viewed along the optic axis, and a curved isogyre pattern when viewed off-axis. These figures allow a trained gemmologist to confirm uniaxial character and, combined with refractive index measurements, to narrow identification to a small number of candidate species.

The crystal system also informs the interpretation of inclusions and growth features. The characteristic growth tubes, hexagonal growth zones, and two-phase inclusions of emerald, for instance, are direct expressions of the hexagonal symmetry of the host crystal's growth environment. Similarly, the silk of fine rubies and sapphires — rutile needles oriented along the three a-axes of the trigonal host — reflects the underlying symmetry of the corundum lattice.