Frieze Patterns

A frieze is a pattern which repeats in one direction. Friezes are often seen as ornaments in architecture. A mathematical analysis reveals that there are seven different frieze patterns possible.


Pattern 1: Translation

The only transformation in this pattern is a translation.


Pattern 2: Glide reflection

The transformation in this pattern is a glide reflection. All frieze patterns also map onto themslves under a translation.


Pattern 3: Two parallel reflections

The transformations in this pattern are two parallel reflections across vertical mirrors..


Pattern 4: Two half turns

The transformations in this pattern are two half turns.


Pattern 5: A reflection and a half turn

The transformations in this pattern are a reflection across a vertical mirror and a half turn.


Pattern 6: Horizontal reflection

The transformations in this pattern are a translation and a reflection across a horizontal mirror.


Pattern 7: Three reflections

The transformations in this pattern are three reflections, one across a horizontal mirror and the other two across parallel vertical mirrors.