Symmetry In One Dimension

Frieze Patterns

The first of these designs is a frieze pattern with translation symmetry only (F symmetry). Put appropriate symbols, modifications of the letter P, in as few cells as possible so that the resulting frieze exhibits the appropriate symmetry. For example, the F symmetry example is already complete.

1. F symmetry (translation only)

P

P

P

P

2. A symmetry (perpendicular reflections and translation)

P

P

P

P

3. B symmetry (midline reflection and translation)

P

P

P

P

4. H symmetry (perpendicular and midline reflections, 2-fold roto and translation)

P

P

P

P

5. N symmetry (2-fold roto and translation)

P

P

P

P

6. MW symmetry (perpendicular reflections, 2-fold roto rotocentres not on reflection lines, translation)

P

P

P

P

7. dq symmetry (glide reflection and translation)

P

P

P

P