Alina and Simon from 2hD architects have had a few meetings with Steve Wickham of Price & Myers engineers to develop the sketches up into a buildable, durable design. The initial design was for the circular roof to be supported by plywood beams radiating out to the posts at the edge, with the beams meeting in a single node in the centre:
Reciprocal frames are created from a closed circuit of mutually supporting elements- each beam leans on another beam. They can span large distances with relatively short beams, and are often found in nature (for example birds' nests). Better still, the geometry can be distorted to cope with the supporting posts being in non-regular locations...
Here's the developed design: