Math in… Papel Picado

Papel picado (“chopped paper”) is a Mexican craft tracing back to an Aztec practice of decorating tree bark. The modern offshoot of this tradition is made by cutting tissue paper. These sheets are strung together into banners to decorate for holidays, weddings, and other special occasions.

Intricate designs are typically etched into several sheets simultaneously using chisels and stencils, but simple designs can be made by folding a sheet and cutting across folds. This can be used to make designs with reflectional symmetries.

What other types of symmetries can you create through folding and cutting?