Twist - Exploring the Cube and its Faces

A recent sculptural undertaking of mine - although it may not seem like it at first, this tangled mess is actually based upon the cube. It's made of 24 empty pen barrels, tied together with rubber bands. There are six square faces, two of each color (the faces of the same color are parallel). Essentially, it is what I think would happen if you took a cube, pushed its square sides inward, and gave them a twist. Below is a single square face -

Then, each of the three pairs of faces are arranged with a π/4 twist, which looks like this when viewed face on -

This arrangement makes eight convenient slots where the other four faces can interlock, as shown here. The darker/opaque green and purple dots indicate how the green and purple squares fit into the blue ones. Imagine that the set of green faces and the set of purple faces both also have a half twist to them. Also, the lighter green and purple dots on the intersection of the green and purple pieces drawn indicate the corners of the faces (the green dots on the purple pieces means the green overlaps there and two green sides come together at that point as a corner, and vice versa for the purple dots on the green pieces). You can actually see this a bit in the first picture of the actual sculpture, where the green and blue faces are held in place by the purple, and how the corners of the blue and green meet up and overlap.

If you turned the piece around, you would see this arrangement three times, once with each color serving as the outer "framework" as the blue is shown here. This was actually quite challenging to assemble, as it became a feat of intense coordination to hold everything together before it was all tied in place, but finished up, it pretty much holds itself together now. I made each of the squares smaller to tighten up the structure and I like how the ends sticking out at each corner give the whole thing a messier look - a curious juxtaposition of order and chaos.