A dipyramid — also termed a bipyramid — is a closed crystal form consisting of two pyramids united at a common equatorial plane, their apices pointing in opposite directions. The resulting solid is bounded entirely by triangular faces that meet at a central girdle, or equator, and converge to a point at each pole. Dipyramids are characteristic of three crystal systems — tetragonal, hexagonal, and orthorhombic — and appear with particular prominence in several commercially important gem species, most notably zircon. Recognising dipyramidal habit in rough material assists the gemmologist and lapidary alike in assessing crystal quality, planning orientation, and understanding the optical and physical properties that flow from a stone's internal symmetry.

Crystallographic Basis

In classical morphological crystallography, a crystal form is a set of faces related to one another by the symmetry elements of the crystal class to which the mineral belongs. A dipyramid arises when the symmetry operations of the class generate a face above the equatorial plane and simultaneously produce a mirror-image face below it, the two sets together enclosing space completely. The number of faces on a dipyramid is therefore always twice the number on the corresponding pyramid of the same system.

Three principal dipyramidal types are encountered in gemmology:

• Tetragonal dipyramid: Eight triangular faces (four above, four below the equator), generated by the fourfold rotation axis and horizontal mirror plane of the tetragonal system. The faces are isosceles triangles; their exact proportions depend on the axial ratio of the mineral. Zircon is the pre-eminent gem example.
• Hexagonal dipyramid: Twelve triangular faces (six above, six below), arising from the sixfold axis and horizontal mirror of the hexagonal system. Quartz, though more commonly recognised by its rhombohedral and prismatic habit, occasionally displays hexagonal dipyramidal terminations, particularly in rapidly grown crystals.
• Orthorhombic dipyramid: Eight triangular faces, but here the three crystallographic axes are all of unequal length, so the faces are scalene triangles rather than isosceles. Topaz and andalusite are orthorhombic gem minerals that may exhibit orthorhombic dipyramidal forms, though typically in combination with prisms and other modifying forms.

Miller Indices and Face Notation

Individual dipyramidal forms are distinguished by their Miller indices, a notation expressing the reciprocal intercepts of a face on the crystallographic axes. For a tetragonal dipyramid, the general form symbol is {hkl} where h, k, and l are non-zero integers; the special form {101} and {111} are among the most commonly observed on zircon. In the hexagonal system, four-index (Miller–Bravais) notation is standard: a dipyramidal face might be written {10͐11} or {11͐22}, reflecting the three equivalent lateral axes and the principal c-axis. These distinctions matter practically because different dipyramidal forms on the same crystal intercept the optic axis at different angles, influencing how a lapidary should orient the table of a finished gem to best display pleochroism or minimise undesirable colour zones.

Zircon: The Canonical Dipyramidal Gem

Zircon (ZrSiO₄) is the gem species most strongly associated with dipyramidal habit. Tetragonal zircon crystals characteristically combine a short prism ({100} or {110}) with prominent dipyramidal terminations, producing the squat, double-pointed shape familiar from rough parcels originating in Sri Lanka, Cambodia, Tanzania, and Myanmar. In many specimens the prism zone is so compressed that the crystal appears almost purely dipyramidal — two four-sided pyramids sharing a narrow waist. This habit is so diagnostic that an experienced buyer can often identify zircon rough on habit alone before resorting to optical or specific-gravity testing.

The dipyramidal faces of zircon frequently display a vitreous to adamantine lustre and, in high-type material, show the strong birefringence characteristic of the species: doubling of back facets is visible to the naked eye through the table of a cut stone, a direct consequence of the tetragonal crystal structure that generates the dipyramidal form in the first place. Metamict zircon — material in which radioactive decay of trace uranium and thorium has disrupted the crystal lattice — loses its sharp dipyramidal faces and may appear rounded or frosted, a useful indicator of elevated radioactivity and altered optical constants.

Other Gem Species

Beyond zircon, dipyramidal forms appear as modifying or subordinate faces on several other gem minerals:

• Quartz: The common hexagonal prism-and-rhombohedron habit of quartz is occasionally supplemented or replaced by hexagonal dipyramidal terminations, particularly in hydrothermal veins where growth was rapid. Such crystals, sometimes called dipyramidal quartz or Japanese twin configurations when twinned, are collected as mineral specimens but are rarely faceted.
• Topaz: Orthorhombic topaz crystals from Ouro Preto, Brazil, and the Ural Mountains, Russia, commonly show the orthorhombic dipyramid {111} in combination with basal pinacoid and prismatic faces. The dipyramidal faces are often striated parallel to the c-axis and provide a useful orientation guide when cleaving rough along the perfect basal cleavage.
• Vesuvianite (Idocrase): Tetragonal vesuvianite from Asbestos, Québec, and Monzoni, Italy, frequently crystallises as short tetragonal prisms capped by dipyramidal terminations, giving crystals a characteristic stubby appearance.
• Scheelite: This tetragonal calcium tungstate, occasionally faceted as a collector's gem, forms distinctive dipyramidal crystals that fluoresce bright blue-white under shortwave ultraviolet — a property exploited in ore prospecting.

Significance in Rough Evaluation and Cutting

Understanding dipyramidal habit has direct practical consequences for the gem cutter and rough buyer. Because a dipyramid is a closed form — it encloses space without requiring additional faces — a single well-formed dipyramidal crystal defines the optic axis orientation unambiguously: the axis of the dipyramid coincides with the crystallographic c-axis, which in tetragonal and hexagonal gems is also the optic axis. Orienting the table of a finished stone perpendicular to this axis, or at a calculated angle to it, is therefore straightforward when the rough retains recognisable dipyramidal faces.

For strongly pleochroic tetragonal gems such as zircon, the choice of orientation relative to the c-axis governs which pleochroic colour dominates the face-up appearance. In blue zircon from Cambodia, for instance, the ordinary ray is a stronger, more saturated blue than the extraordinary ray; cutters typically orient the table perpendicular to the optic axis to maximise the blue body colour, a decision made easier when the dipyramidal habit of the rough clearly indicates the axis direction.

Dipyramidal faces also provide clues to internal features. Growth zones in zircon often follow the geometry of successive dipyramidal forms, producing concentric colour banding visible under the microscope. Inclusions trapped at the boundaries between prism and dipyramid zones can indicate the thermal history of the crystal and, in some cases, assist in geographic origin determination.

Dipyramid versus Related Forms

The dipyramid should be distinguished from superficially similar closed forms:

• A pyramid is a single-ended form (open at the base) requiring a complementary form to close the crystal; a dipyramid is self-closing.
• A rhombohedron, characteristic of the trigonal division of the hexagonal system, consists of six rhomb-shaped faces and can resemble a distorted dipyramid, but its faces are parallelograms rather than triangles and it belongs to a lower symmetry class. Calcite and tourmaline provide familiar rhombohedral examples.
• A scalenohedron, also trigonal, has twelve scalene triangular faces arranged in a zig-zag pattern around the equator; it is sometimes colloquially called a "dog-tooth" form and is common in calcite.

These distinctions are not merely academic: the symmetry class implied by each form determines whether a mineral can be piezoelectric, pyroelectric, or optically active — properties of direct relevance to gem identification and to the behaviour of stones under polarised light.

Further Reading

• GIA Gems & Gemology — Zircon from Cambodia
• International Gem Society — Zircon Gem Information
• International Gem Society — Topaz Gem Information