Page 77 - Materials Chemistry, Second Edition

64 2 Solid-State Chemistry

Table 2.7. Common Symbols Used for Space Group Representations
Symmetry operation Symbols
Mirror plane (m) ⊥ plane
of projection
Glide plane (a, b, c) ⊥
plane of projection
Glide plane (n) ⊥ plane
of projection
Mirror plane (m) // plane
of projection

Glide plane (a, b, c) // plane of
projection (translation of
1/2 in the direction of
the arrow)
Glide plane (n) // plane of
projection (translation
of 1/2 in the direction
of the arrow)
Rotation axes ⊥ plane
of projection
Screw axes ⊥ plane
of projection
Rotation axes // plane
of projection
Screw axes // plane
of projection
Center of symmetry
(inversion center: i)
Rotation axis ⊥ plane
of projection with center
of symmetry

Points A–D, E–H, I/J, and K/L are equivalent positions in the unit cell, as they are
duplicated by translations of one full unit along a or b. The relationship between
points A and E looks like a simple twofold rotation axis; however, these points differ
by 1/2 a unit cell length in the c-direction. Next, let’s consider the relationship
between points E and I. The apostrophe symbol indicates these points are mirror
images of each other, suggesting that a mirror plane passes between them. However,
these points also vary in their position along c, which implies the presence of a c-
glide plane. Lastly, let’s consider the relationship between points A and I (or E and
L), which are located at the same position along c. To generate position I, one could
mirror point A across the a-axis, followed by translation of 1/2 along a – an a-glide