Line Groups

The following pattern forms take a motif and translate, reflect, rotate and glide reflect the motif along a long line.  Think ducks in a row, then in a double row, or upside-down row.

Below are examples of the t2mg line group from Peter Steven's Handbook of Regular Patterns.  Examine the patterns.  What are the rules of the t2mg line group?

t2mg

There are 7 different formulas for the symmetry line groups.  Check out the letter b examples for each line group.

Symmetry Operations

Symmetry Operations determine how an asymmetrical motif translates across an axis to form a symmetrical motif.  There are four symmetry operations, Translation, Rotation, Reflection and Glide Reflection.  These operations can be applied across a vertical, horizontal or diagonal axis.

Check out the examples below using the simple letter form b.

Horizontal Translation

Vertical Translation

Diagonal Translation

Rotations

Horizontal Reflection

Vertical Reflection

Diagonal Reflection

Glide Reflections