Frieze Groups

Lengthwise, a frieze pattern may have reflection symmetry or just translation symmetry.

Crosswise, it may have reflection symmetry, glide reflection symmetry, halfturn symmetry or no symmetry.

There are many different combinations of these symmetries that can be found in frieze patterns. For example, it might have translation symmetry lengthwise and reflection symmetry crosswise. Or, it could have reflection symmetry lengthwise and no symmetry crosswise. Or, it could have some other combination of lengthwise and crosswise symmetry.

Each possible combination of symmetries is called a frieze group. It turns out that there are 7 different unique frieze groups. (We can prove this, but that's another exercise.)

     Hop       



     Spinhop   



     Jump      



     Sidle     



     Step      



     Spinjump  



     Spinsidle

The exercises on the next two pages will help you figure out which frieze groups have which symmetries.