The device is able to only use five sensors to infer which face is shown — instead of the nine that would be required to discreetly sense each pip location — by taking advantage of a die’s symmetry.
The build was first prototyped on perfboard, then designed into two PCB versions — one with a shift register for increased accuracy, one without. Schematics, along with demo code, are found in the project’s writeup. The team also created a few accessories for the board, including a stepper-driven paddle wheel to push the die into the correct position, and a contraption that rotates into an orientation corresponding to the face detected.
As you might suspect, figuring out how to actually read a die like this took a quite a bit of research and pondering, and the inspiration came from a 2009 Make: post. This nearly 10-year-old version can be watched below, revealing the number detected on a 7-segment display.