1. The problem asks to describe the transformations that map a frieze pattern onto itself. 2. Frieze patterns are infinite strips with repeating motifs. The transformations that map the pattern onto itself include translations, glide reflections, reflections, and rotations. 3. Translation moves the pattern horizontally by the length of one repeat unit, so the pattern aligns perfectly with itself. 4. Reflection flips the pattern over a vertical or horizontal axis that passes through the pattern, preserving the design. 5. Glide reflection combines a translation along the strip with a reflection across a line parallel to the strip. 6. Rotation involves turning the pattern 180 degrees around a point on the strip, mapping the pattern onto itself. 7. Each frieze pattern can have a combination of these symmetries depending on its design. Final answer: The transformations that map the frieze pattern onto itself are translations, reflections, glide reflections, and 180-degree rotations along the strip.