24 Kites Solid Puzzle

The 24 faces of a Deltoidal Icositetrahedron are kites. Choose one out of four positions for each side: R=right from center, RR=far right from center, L=left from center or LL=far left from center. With gaps at the chosen positions you can get 4^4=256 different triangles. If all positions are different we get 4*3*2*1=24 different kites just enough to cover the surface of the solid with L-R and LL-RR matching edges.
It seems to be clever to arrange the pieces like a net of the surface and check for matching edges. After this the whole solid can be constructed with matching edges fixed by U-clips. I chose the net of an octrahedron and replaced each triangle by three kites.