All materials for my upcycle project have been selected. I will be utilizing scrap quarter inch black acrylic for the majority of the construction. I have additionally found some scrap wooden rods with enough length to cut 12 six inch pieces. This is just under double what is required. Below is the CAD model I will utilize to laser cut all of the acrylic pieces.
The top cylinder acts as the dial to open each face. The top and bottom plates are composed of 3 layers of acrylic. This accounts for plenty of space for the bearings, which are just over a quarter inch. Here as another view of the CAD assembly:
The bottom and top plates each hold ball bearings to allow the wooden rods to rotate freely. The wooden rods (7) have been cut to length, including a smaller one to support the dial. Additionally, 20 cheap ball bearing have been purchased. I have prototyped a few versions of the gears (which will also be acrylic), because of the specific design constraints, the gears must be designed from scratch. While my first attempt was not successful, my second attempt will likely be suitable for the final product.