Rhombic Dodecahedron

thingiverse

The 12 faces of a Rhombic Dodecahedron are rhombs. Choose one out of three positions at each side of the rhombs: R=right from center, L=left from center or C=center. With gaps at the chosen positions you can get (3^4+3^2)/2=40 different rhombs. Only 12 rhombs are needed to cover all faces. Therefore I took the subset of pieces with gaps at the same position of three sides and one gap at another position of the fourth side. Now we have 4*(3*2)/2=12 pieces just enough to cover the surface of the solid with L-R and C-C 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.