I recently saw these HyperQBS on Geobender.com, given that they are currently out of stock and I've never been very good at waiting I decided to make my own. Check out the video (hidden in the above)
From the description we know it's 12 identical pyramids that form a cube. We can see the outside lines of the cube (each face splits across the diagonal) and it's safe to assume that all the pyramids meet in the middle so it is relatively straight forward to figure out the geometry and make a 3D model of 1 pyramid.
A quick flit through Pepakura turns the 3D pyramid into a 2D flat paper shape with tabs in all the right places.
Export from Pepakura into a vector file format and it's just a quick trip to the laser cutter to make 12 pyramid shapes that are ready to be glued and assembled together.
I've attached a pdf containing the 2D flats to make your own HyperQBS.
Step 1: Assembling the HyperQBS
Take each flat shape and assemble it into pyramid, once you have 12 of these shapes you can begin assembling them into the HyperQBS.
Used sticky tap to hold the pyramids together. Place tap on either side of the join. The Pyramids should be joined on the right angled sides. The images demonstrate the exact pattern for tape placements, once all 12 are taped together then simply loop the last shape back to the first one.
Step 2: Make Your Patterns
All being well you should have a completed HyperQBS, now start flexing the box to your will and experimenting with the different shapes you can make.