Here I present the edge-based version of my previous 'Purinahedron'. (As Daniel Kwan pointed out, this structure can be interpreted as a sort of irregular dodecahedron, but I prefer naming it after Ralston-Purina's corporate logo. If you see the logo, I am sure that you will agree!) Since the polyhedron exposes 78 squares to the outside world, there are (78 * 4)/2 = 156 Sonobe modules in all.
I tried to assemble this using 12 different colors of Sonobe module--that is, one color for each relative edge position in the 14 individual cubes. But each cube shared at least 3 edges with neighboring cubes, leading to dozens of ambiguous color choices for which two different colors were both "correct". The out-of-place pink and purple squares in the picture were just two examples of these ambiguities.
As a final note, I'm dissatisfied with the quality of photographs I'm getting with our Canon PowerShot A470. Our previous Panasonic DMC-FX3 took much sharper photographs, though its images had a slightly lower resolution. I'll have to look into that later.