RHOMBOHEDRAL CRYSTAL SYSTEM

(Redirected from Trigonal symmetry)

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 diagonal along a body. a=b=c; alpha=beta=gamma unequal to 90°.
In some classification schemes, the 'rhombohedral system' is grouped into a larger hexagonal system.
There exists only one 'rhombohedral' Bravais lattice.

Contents

List of particulars

References

List of particulars

The point groups which fall under this crystal system are listed below, followed by their representations in international notation and Schoenflies notation, and example crystals.
{| cellpadding=8
|'name'
|'international'
|'Schoenflies'
|'examples'
|-
|rhombohedral holohedral
|$overline\{3\}m$
|''D_3d''
|calcite, corundum, hematite
|-
|rhombohedral hemimorphic
|$3m$
| ''C_3v''
|tourmaline, alunite
|-
|rhombohedral tetartohedral
|$overline\{3\}$
|''S₆''
|dolomite, ilmenite
|-
|trapezohedral
|$32$
|''D₃''
|quartz, cinnabar
|-
|rhombohedral tetartohedral
|$3$
|''C₃''
|none verified
|}

References

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