Pyramid — Crystal Form Defined by Convergent Faces Meeting at an Apex
Pyramid — Crystal Form Defined by Convergent Faces Meeting at an Apex
A fundamental crystallographic form classified by its symmetry and number of faces
A pyramid in crystallography is a closed or open form composed of three or more non-parallel faces that converge at a single point, the apex. Pyramids are among the most familiar of crystal forms because their geometry is intuitive and because their development on natural crystals produces the pointed terminations that allow rapid recognition of mineral species in the field. In gemmology, pyramidal terminations are diagnostic features used in rough sorting and crystal identification, and their angles relate directly to the underlying symmetry of the crystal system.
Classification by symmetry
Pyramids are classified by the crystal system to which they belong and by the number of faces meeting at the apex. A trigonal pyramid has three faces and arises in crystals of the trigonal system. A tetragonal pyramid has four faces and is characteristic of the tetragonal system, found in zircon and scheelite. A hexagonal pyramid has six faces and is typical of the hexagonal system; pyramidal terminations on quartz crystals — though quartz belongs to the trigonal system — appear hexagonal because the pyramid faces alternate with rhombohedral faces of similar inclination, producing a six-sided termination. A ditetragonal or dihexagonal pyramid has eight or twelve faces respectively and arises in higher-symmetry classes within the tetragonal and hexagonal systems.
The orthorhombic, monoclinic, and triclinic systems also exhibit pyramidal forms, though with progressively lower symmetry the pyramids become more irregular and less obviously recognisable as classical pyramids. In the cubic system, pyramidal forms are subsumed into the higher-symmetry forms such as the tetrahedron and octahedron, both of which can be regarded as combinations of trigonal pyramids related by cubic symmetry operations.
Dipyramids and combinations
A dipyramid is a closed form consisting of two pyramids joined base-to-base across a horizontal mirror plane. Quartz crystals frequently terminate in apparent hexagonal dipyramids — although strictly the termination consists of positive and negative rhombohedra rather than true hexagonal pyramid faces. Zircon, a tetragonal mineral, displays well-developed tetragonal dipyramidal terminations on prismatic crystals. Spinel and diamond, both cubic, can be described as octahedral, which is a special case of a trigonal dipyramid in cubic symmetry.
In natural crystals, pyramids rarely occur in isolation. They combine with prismatic, pinacoidal, and rhombohedral forms to produce the multi-faceted habits seen in mature crystals. The relative development of pyramid versus prism faces is a function of growth rate, temperature, and chemistry of the crystallising fluid, and produces the characteristic appearance of crystals from particular localities — Herkimer quartz dipyramids and Mogok zircon double-terminated tetragonal dipyramids being two well-known examples.
Diagnostic features
Pyramidal faces often display growth striations parallel to the base of the pyramid, the result of stepped growth during crystallisation. These striations are diagnostic in some species: the horizontal striations on quartz prism faces and the chevron-like patterns on tourmaline pyramidal terminations are widely used field-identification clues. Pyramidal faces may also exhibit etch figures, surface pits with shapes constrained by the underlying crystal symmetry, that arise from partial dissolution after crystal growth ceases.
Inter-facial angles between pyramid faces are constant for a given mineral species and crystal system, and were historically measured with a contact goniometer or optical goniometer to confirm species identification before modern analytical techniques became available. The constancy of these angles is one expression of the law of constancy of inter-facial angles, the founding principle of mineralogical crystallography established by Romé de l'Isle and Haüy in the eighteenth century.
In gemmology
Pyramidal terminations on rough crystals influence cutting decisions. A well-developed dipyramid on a quartz or zircon crystal often points to the optic axis and provides the cutter with an immediate orientation for placing the table of a faceted stone perpendicular to the c-axis, minimising visible birefringence in the cut gem. For crystals where pyramidal forms dominate the habit, brilliant and step cuts oriented along the pyramidal axis usually offer the best yield from the rough.
The natural pyramid faces themselves are sometimes preserved in finished pieces, particularly in mineral specimens cut as gems where the upper crystal termination is left intact and only the lower portion is faceted or polished. Topaz crystals from Brazil and aquamarine from Pakistan are sometimes finished this way, retaining the natural pyramid as a design feature.