This decorative modular fold is also a spectacular action model: Smack it into the air, and it literally explodes in a cloud of butterflies.
Click here to view a gif with the butterflies in action.
As can be seen from the diagram, just 12 simple waterbomb bases are used, making the folding very easy. The subsequent assembly requires patience, but follow the description and it should not be too difficult.
Kenneth Kawamura who designed the butterfly ball, explains that many variations can be made. He, Joe Powers and most likely other people have found many such. For instance 6 preliminary bases may also be put together into a ball. Try it yourself!
Kenneth also explains that originally it was named "butterfly bomb", but that "butterfly ball" today is more common because some people objected to the "bomb" connotations because the Japanese during World War II spread something also called a "butterfly bomb". In Danish, however, I have chosen to stick to the much more descriptive "sommerfuglebombe" (=butterfly bomb) because I find it comforting that in origami bombs only spread water (see the waterbomb and its winged form) and butterflies. Moreover, the word "sommerfuglebombe" is not used in Danish in the World War II sense.
There is a good description of the butterfly bomb as a cubeoctahedron in Thomas Hull: "Project Origami: Activities for Exploring Mathematics", A.K.Peters, 2006, ISBN 978-1568812588.