As mentioned, the Nivi style is just one of many methods of draping a sari. Depending on which part of India they live in, women may drape their saris differently from region to region. Some styles are similar to others. For example, women in Gujarat drape their saris similarly to the Nivi style, but the pallu falls over the right shoulder instead of the left, and it is also draped from back to front instead of front to back.
