the lines that are used to push down the point are approximates in the CP. Feel free to move around some things until you get something that works. A bit difficult for a CP as I haven't made this before (the points on CP); however, I did discover that the color of the points can be changed to white very easily for a possible stylistic effect. I may try this later.
The Sliding Cubes is one of the few times I attempted to design a model with a goal in mind. I wanted points to protrude out of the simple cube shape in order to connect two Jo Nakashima seamless cubes together. The first time I tried this, I ended up with points that were half the box wide. I actually accidentally discovered the collapsing mechanism that led to the first time I was able to make points. From there, the model has been refined slowly and new models, such as the Sliding Cubes 3 (restructured), have been made using two/three pieces of paper.