We found a new way to connect the circles: Shapes designed to hold a circle each, cut out of a latex sheet by the laser cutter. A trial-and-error-approach was used to find the optimal shape. Each of the latex shapes has to be connected to six other latex sheets to form a surface. The material stretches, which provides a flexible, yet stable surface.
A new problem soon emerged, though: Connecting the latex shapes. We tried different solutions, and ended up designing a whole new component to be placed as an interlocking joint between the latex shapes, as shown in the photo below.

We went through a process of testing different component designs, and ended up with the design to the right in the picture below.

The components are made of acrylic glass as shown below.

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