
We’ve recreated all five pieces of the Curved Space for 3D printing, transforming them into a toy. The goal was to explore the challenges and problems of the structure on a small scale in order to better understand what needs attention when scaling up.
The toy consists of five different modules and a one universal connector that can link all the parts together. For our first experimental assemblies, we used 11 saddle pentagons, 4 saddle hexagons, 3 hexagons, and 4 squares. In the first step we generated 16 different assembly variations. Throughout our experiments, we aimed to generate closed loops to ensure structural stability.

One of the main challenges was the thickness of the parts. As Peter Pearce pointed out in his work:
“The ideal minimal surface is a structure of zero thickness. The surface modules used in the present application have a typical wall thickness of 0.190 inches. The translation of the zero thickness of the ideal minimal surface to a surface module of such a thickness is a technical problem of considerable complexity. The difficulties of such a problem are further compounded by the need to incorporate into the surface modules means by which structures can be assembled. In order to preserve the structural integrity of the branched-shell structures, whatever connector system that is used must provide membrane continuity throughout an assembled labyrinth.” ( Structure in Nature is Strategy for Design, Peter Pearce, Page 231)
We generated parts with a thickness of 2.4 mm and diameters of 80mm, which already hinted at the challenges we would face. We also decided to leave larger gaps for the connectors to ensure we had some room for tolerances and flexibility, but this brought its own set of issues.

As we experimented with different assemblies, we encountered a significant challenge: the connection gaps were not consistent.

In some regions, the parts touched, creating unwanted friction, while in other areas, the gaps were wider than expected, leading to instability. This misalignment made it difficult to achieve a seamless assembly, and it was even more challenging when attempting to add more parts to the structure.
Several factors contributed to this inconsistency:
- Movable Connector: The connector was not always perfectly centered, which caused uneven gaps between opposite parts.
- Rotation of the Connector: As the connector could rotate during the assembly process, two seemingly identical connections could end up with different alignments of the connector.
- Increasing Complexity: As the number of parts increased, the misalignment of the gaps became more pronounced. The more parts we added, the harder it became to maintain consistent gaps, which in turn made assembly increasingly difficult.

By combining four saddle pentagons, it’s possible to construct a saddle octagon. However, due to the loose connections and lack of fixed angles, the resulting structure is weak. As shown in the following image, the connection is weak, and the part can easily kink along its two middle axes

This reconstructed toy is inspired by the Curved Space game, which is based on the curved space diamond structure. Through this process, we’ve come to appreciate the challenges of assembling a stable configuration. Interestingly, this might explain why, in the game, the parts are simplified. Rather than constructing the saddle octagon from four individual saddle pentagons, it’s treated as a single component, likely to reduce complexity and improve stability.
