SymmetryWorks Mini-Tutorials

# Determining the Type of Symmetry of a Repeating Pattern

How do you find the symmetry type of a pattern? Easy: by answering at most four questions, starting with this one: Will the pattern coincide with itself if it is rotated around some center? Is there a reflection? Is there a glide-reflection? Simple shift (p1)  Glide reflection (pg)  Is there a glide-reflection in an axis that is not a reflection axis? Mirror (pm)  Mirror & glide (cm)  Is there a reflection? Is there a glide-reflection? Half-turn (p2)  Double glide (pgg)  Are there reflections in two directions? Parallel mirrors & glide (pmg)  Are all rotation centers on reflection axes? Perpendicular mirrors & glide (cmm)  Double mirror (pmm)  Is there a reflection? Three rotations (p3)  Are there reflections in two directions? Three rotations & mirrors (p31m)  Three mirrors (p3m1)  Is there a reflection? Pinwheel (p4)  Are there four reflection axes? Quarter-turns & rotated mirrors (p4g)  Quarter-turns & mirrors (p4m)  Is there a reflection? Six rotations (p6)  Kaleidoscope (p6m) Adopted from McLenaghan and Levy, 1996, p. 264.