Rhombohedral crystal system

In crystallography, the rhombohedral (or trigonal) crystal system is one of the seven lattice point groups, named after the two-dimensional rhombus. A crystal system is described by three basis vectors. In the rhombohedral system, the crystal is described by vectors of equal length, of which all three are not mutually orthogonal. The rhombohedral system can be thought of as the cubic system stretched diagonally along a body. a = b = c; $alpha\; =\; beta\; =\; gamma\; neq\; 90^circ$. In some classification schemes, the rhombohedral system is grouped into a larger hexagonal system.

There exists only one rhombohedral Bravais lattice.

List of particulars

The point groups which fall under this crystal system are listed below, followed by their representations in international notation (Hermann-Mauguin notation) and Schoenflies notation, and example crystals.

name	international	Schoenflies	examples
rhombohedral holohedral	$overline\{3\}m$	D3d	calcite, corundum, hematite
rhombohedral hemimorphic	$3m$	C3v	tourmaline, alunite
rhombohedral tetartohedral	$overline\{3\}$	S6	dolomite, ilmenite
trapezohedral	$32$	D3	quartz, cinnabar
rhombohedral tetartohedral	$3$	C3	none verified

See also

• Crystal structure

References

• Hurlbut, Cornelius S.; Klein, Cornelis, 1985, Manual of Mineralogy, 20th ed., pp. 78 - 89, ISBN 0-471-80580-7