Details

When you select the "show highlighted motif" option, one motif appears in blue and the one immediately to its left appears in red. This lets you see the action of a reflection, rotation, or translation more easily. The axes of reflection used go through the center point of the blue motif, and that point is the center of the rotations as well. Note that in the case of a border pattern of type mg the vertical axis over which the border pattern has symmetry is not through the center of the motif (see Snapshot 5).

All border patterns have translational symmetry. Border patterns are classified according to which other symmetries they exhibit. The seven symmetry types of a border pattern are:

11: no other symmetry

m1: reflection over a vertical axis, but not a horizontal axis

1m: reflection over a horizontal axis, but not a vertical axis

12: rotation by 180 degrees, but no reflection symmetry

mm: reflection over both a horizontal axis and a vertical axis (which implies rotational symmetry)

1g: glide reflection, but no reflection

mg: reflection over a vertical axis and glide reflection (which implies rotational symmetry)