How do you make the winged sonobe module?
Take two ordinary modules and join them together with one of their tabs in one of the other's pockets, forming the analogue of a triangular pyramid but with two sides only. 

You obtain a subassembly that looks and works like a single Sonobe module, with the same tabs and pockets in the same position (the unused half of each module) and an additional triangular fin (formed by the joined halves of the modules) protruding from the outer side.  

Make a plain old pyramidated octahedron with these assemblies replacing the regular modules and you'll get the 8 pyramids and 12 fins in the photo.