The Hexagonal System: Beryl, Apatite, Graphite and Six-Sided Crystals
The hexagonal system has a single c axis and two equal axes at 120° in the basal plane. Beryl (emerald, aquamarine), apatite and graphite belong here; quartz is trigonal.
Key points
| Axes | a = b ≠ c (two equal axes in a plane, with a perpendicular c axis) |
|---|---|
| Angles | α = β = 90°, γ = 120° |
| Characteristic symmetry | One six-fold rotation axis |
| Symmetry classes | 7 of 32 |
| Bravais lattice | 1 (primitive) |
| Typical minerals | Beryl, apatite, graphite, molybdenite, vanadinite, pyromorphite, sugilite, ice |
| Common pitfall | Quartz is trigonal, not hexagonal |
Six sides, six faces, a six-fold axis
In the hexagonal system, the unit cell has two equal axes, a and b, which form an angle of 120° with each other, and a third axis, c, perpendicular to their plane and of a different length. Its hallmark is a six-fold symmetry axis: a turn of one sixth of a circle around c leaves the crystal unchanged. Hence the six-sided prism silhouette associated with beryl, and the six-sided plates of graphite.
Ice is a good everyday example: it is a mineral in the strict sense, and six-armed snowflakes reflect its hexagonal lattice. Johannes Kepler had already puzzled over this symmetry in 1611, in a short treatise on the six-cornered snowflake.
Axes and angles
| Quantity | Value | Remark |
|---|---|---|
| Lengths | a = b ≠ c | The c axis is unique |
| Angles | α = β = 90°, γ = 120° | a and b are at 120° in the basal plane |
| Symmetry | Six-fold axis | At least one six-fold axis |
| Classes | 7 | Including the richest class, 6/mmm |
| Lattice | 1 (P) | A single Bravais lattice |
To describe faces, crystallographers sometimes add a third axis in the basal plane (the Miller-Bravais indices, written hkil, with h + k + i = 0). This four-figure notation reflects the six-fold symmetry.
Hexagonal or trigonal? A matter of convention
This is the point that most confuses beginners. Quartz, tourmalines, calcite and corundum (ruby, sapphire) have crystals that look like six-faced prisms, and yet they belong to the trigonal system, because their mandatory symmetry is a three-fold axis, not six. See the trigonal system.
Textbooks differ in how they present this. Modern crystallography distinguishes seven systems, including hexagonal and trigonal. But the two share the same unit-cell shape, and they are grouped together in a single hexagonal family; older manuals and some websites therefore speak of only six systems. This page follows the seven-system presentation, the most common one. A curious case: alpha quartz, the form found in our stones, is trigonal, but above about 573 °C, at ordinary pressure, it transforms into beta quartz, which is hexagonal.
Hexagonal minerals: reference points
| Mineral | Simplified formula | Mohs hardness | Density | Habit |
|---|---|---|---|---|
| Beryl (emerald, aquamarine, morganite, heliodor) | Be3Al2Si6O18 | 7.5 to 8 | 2.6 to 2.9 | Elongated prisms with six faces |
| Apatite | Ca5(PO4)3(F,Cl,OH) | 5 | 3.1 to 3.2 | Short hexagonal prisms |
| Graphite | C | 1 to 2 | 2.1 to 2.2 | Hexagonal plates |
| Molybdenite | MoS2 | 1 to 1.5 | about 4.7 | Hexagonal flakes |
| Vanadinite | Pb5(VO4)3Cl | 2.5 to 3 | 6.8 to 7.1 | Reddish-orange prisms, contains lead |
| Pyromorphite | Pb5(PO4)3Cl | 3.5 to 4 | about 7 | Green or yellow prisms, contains lead |
| Sugilite | silicate of potassium, sodium, iron, manganese and lithium | 5.5 to 6.5 | 2.7 to 2.8 | Massive, violet |
Apatite’s hardness of 5 is precisely the fifth reference point on the Mohs scale. Beryl, which is harder, is fairly brittle: an emerald full of fissures (a “garden”) can break on impact despite its hardness of 7.5 to 8. See our pages beryl, emerald, aquamarine and apatite.
Graphite and diamond: the same carbon, two architectures
Graphite and diamond are both made of pure carbon, but their structure changes everything. In graphite (hexagonal), the atoms form flat sheets with hexagonal meshes, where the bonds are short (about 1.42 Å); these sheets are stacked about 3.35 Å apart and slide easily over one another. Hence the hardness of 1 to 2, the grey streak on paper, and its use in pencil leads. In diamond (cubic), each atom is bonded to four neighbours in a tetrahedron, hence a hardness of 10. Two minerals of the same composition but different structures are called polymorphs.
Spotting the hexagon at home
A few harmless ideas: look through a magnifying glass at a small quartz or tourmaline crystal and count the side faces (six, but of two kinds, which gives away the trigonal system); observe the cross-section of a beryl or aquamarine prism; look at a snowflake on a dark cloth; or rub a pencil on a sheet of paper and examine the graphite powder, which is made of tiny flakes, through a magnifying glass. By contrast, avoid any flame or acid test on a stone you want to keep: heat can crack it.
Frequently asked questions
Which minerals are hexagonal?
Beryl (emerald, aquamarine, morganite), apatite, graphite, molybdenite, vanadinite, pyromorphite, sugilite and ice.
Is quartz hexagonal?
No, at ordinary temperature it is trigonal. Its crystals look like six-sided prisms, but its mandatory symmetry is a three-fold axis. It only becomes hexagonal above about 573 °C.
Why do some books count six crystal systems and others seven?
Because trigonal and hexagonal share the same unit-cell shape. Grouping them gives six families; separating them according to their own symmetry gives seven systems.
Is emerald fragile?
It is hard (7.5 to 8) but often cracked by its inclusions, so it is sensitive to knocks. Avoid striking it and do not clean it with ultrasound.
What is the difference between graphite and diamond?
The same carbon atoms, but different structures: hexagonal sheets that slide over one another in graphite, and a rigid three-dimensional lattice in diamond.
Also read
The meanings mentioned belong to tradition and symbolism. They are neither promises of results nor medical advice. Back to Mineralogy for beginners.