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.