The symmetry of
crystals. Symmetry elements
The symmetry elements in
crystals are geometric operations by means of which we
relate an atom (ion, or molecule), located in the unit
cell, with other
ones that are equivalent (symetrically equivalent). To represent the symmetry
elements in crystallography we use
graphical and numerical symbols as shown in the following
table…
Below you will also find several examples of symmetry elements
applied
to the repetition of objects, in this case represented by a hand, or a
circle...
Numeric and
graphical symbols for the symmetry elements
Making use of some
animated representations made available at the Bucknell University,
we represent here (with no animation) some of the most common
operations of the symmetry elements, using hands and circles:
Two-fold axis 2
Three-fold axis 3
Four-fold axis
4
Six-fold
axis 6
Two-fold screw axis
2_{1}
Mirror plane m
Glide plane
a, b, c
Inversion center
1
The two
blue-colored hands (left hands) are on a lower plane than the white
ones (right hands).
Four-fold improper axis of
rotation 4
But let's
go back...