Crystals are formed by a unit cell which repeats in 3 dimensions.
The symmetry of this cell occurs in 7 distinct systems, depending
the cell shape and symmetry. Symmetry is influenced by the cell shape
(eg. a non-cubic cell will never have cubic symmetry) and the layout
of the atoms within the cell.
Small (but regular) displacements of atoms within a cell due to
temperature and/or pressure, can and do change the symmetry of a
The cell dimensions are usually named "a,b,c". Where one is of different
length to the other or is otherwise "special", this is usually labelled
A crystal system where the cell dimensions are equal, and all inter-axis
angles are 90deg. It is characterised by
3 tetrads (axes of 4-fold rotational symmetry) and 4 triads (axes of
3-fold rotational symmetry) plus associated diads (2 -fold symmetry)
and mirror planes.
This has the highest form of symmetry possible.
A crystal system characterised by the presence of a hexad (axis of
6-fold rotation). Two of the axes are 120deg apart and are of equal
length. The third axis (c) is aligned with the hexad, and is 90deg
to the other two axes.
A crystal system where the cell dimensions (a,b,c) are of unequal
length. Two of the axes are at 90deg to each other, whilst the third is
A crystal system where the cell sizes (a,b,c) have different lengths,
but all of the inter-axis angles are 90deg. This has no tetrads
(axes of 4-fold rotational symmetry) or triads (axes of 3-fold
symmetry). It does have 3 diads (axes of 2-fold symmetry), centred in
the middle of each face.
A crystal system where two of the cell sizes are equal (a & b) whilst
the other (c by definition) is of a different length. All inter-axis
angles are 90deg.
This has one tetrad (axis of 4-fold rotational symmetry) and no
triads (axes of 3-fold rotational symmetry), but does have 2 diads
(2 fold rotational symmetry).
By setting the length of c to that of a&b, the system becomes cubic.
By setting a, b, and c to different lengths, the system becomes
A crystal system where the three cell dimensions are unequal length,
and none of the corresponding axes are at 90deg.
This is the lowest form of crystal symmetry possible.
This is a crystal system which is similar to the hexagonal system.
This is characterised by a triad (axis of 3-fold rotation). Two of
the cell axes are 120deg apart, and are both 90deg from the c axis which
is aligned with the triad.