# 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.

[Transformations]
[Plane Symmetry] [Geometry] [Resources]

Maintained by David A. Reid

Email: *david.reid@acadiau.ca*

Last modified April 4, 2003

http://socrates.acadiau.ca/courses/educ/reid/Geometry/Symmetry/frieze.html