Pattern design on Illustrator
SymmetryWorks Mini-Tutorials

Basic Symmetry Operations

Is there a reflection? What is a glide-reflection? What other operations are used in the pattern design? There are only four basic operations that bring about an unending variety of symmetric patterns: translation, rotation, reflection, and glide-reflection. Here's the symmetry lingo at a glance. You can use SymmetryWorks to experiment with each symmetry type.

Simple shift


(reflection + translation)

180° (half-turn) rotation
around a two-fold rotation center

120° (1/3-turn) rotation around a three-fold rotation center

90° (quarter-turn) rotation around a four-fold rotation center

60° (1/6-turn) rotation around a six-fold rotation center