There are 18 different wing designs that Vivillon can have on its wings. It ranges mainly in color and style based on what region that 3DS is registered/set. From each area, it differs based on the region's climate, continent and even the top most popular countries on earth.
Vivillon and Arceus are tied with having the second widest variety of Pokémon Forms, having a total of 18. They are bested by Unown by 28 forms.
There are 2 unused forms of Vivillon.
Vivillon's name comes from "vivi", which is translated as "lively" and "papillon", which is "butterfly".