Thanks for both videos - the commercial as well as behind the scene. A clarification about the shape. In origami we loosely call the Sonobe type constructions stellated octahedron (12 units) or stellated icosahedron (30 units) while they are actually not. The the single sheet model in the ad appears to have the same shape as a 12 unit Sonobe construction.
A stellated octahedron can be thought of as a compound of two tetrahedra, where the spikes are smaller tetrahedra themselves ( https://en.wikipedia.org/wiki/Stellated_octahedron). The Sonobe constructions have spikes that are pyramids bound by 3 right isosceles triangles and a triangular base. In the case of the Stellated Octahedron, the spikes are bound by 4 equilateral triangles. The Sonobe type constructions in no way satisfy the criteria for a stellated solid ( https://en.wikipedia.org/wiki/Stellation). But then, I haven't found a good name for those Sonobe solids. How about pyramidized octahedron or icosahedron? Meenakshi