It turns out that a frieze may possess one of exactly 7 different symmetry types. A trail of footprints counts as a frieze decoration. Now that we've met the 7 types, let's review some of their features. HOP possesses only translation symmetry to the left and right. JUMP possesses a line of reflection running along the middle of the strip.
Reflection occur between consecutive footprint.
One sort lies close to the big toes, the other close to the little toes. WALK possesses a line of glide reflection running along the middle of the strip. SPIN-JUMP possesses a line of reflection running along the middle of the strip. SPIN-HOP has no reflections or glide reflections, but does have two types of order 2 gyration points. Some lie midway between nearby big toes, some midway between nearby heels.