The Rube Goldberg Model
This model was completed in Jan., 2006. It¡¯s a sequel to the spidermath model which although interesting, seemed unlikely as something which would ever get built in a fullscale version. The model is based on two equalangle polyhedra with chord factors provided by Joe Clinton in his ¡°Equalangle conjecture¡± paper. I call them ¡°equaledge¡± polyhedra which amounts to the same thing. The model uses an inflated hemisphere (ripstop nylon) as staging for the floppy stages of construction. Click on photos to enlarge 

1) The hemisphere being inflated, with a partial grid laid out flat, beginning to settle into a spherical shape. 

2) The inner equal edge grid, triangulated, showing hubs with empty prongs for connecting to diagonals to the outer grid. 

3) This shows a phase of construction involving many fudgefactors. Not knowing how to derive the triangulation chords mathematically, I arbitrarily decided to have the radius of the outer shell be 5¡± greater than the inner shell, and made some 5¡± posts to support the outer equaledge polyhedron. 

I think of these breakdowns as being analogous to a 4frequency triacon for the inner shell, and a 6freqnency alternate for the outer shell. Its fascinating, but becomes intuitively obvious, that the different equaledge grids relate in pairs which allow for triangular connection.  
4) The chord lengths of the diagonals were set empirically by seeing what seemed to fit between the inner and outer shells. There were three lengths in the inner grid (one for the ¡°equal edge¡± length, one for the pentagon spokes and one for the hexagon spokes). 

There were two lengths for the diagonals (one connecting the pents of the outer grid to the pents of the inner grid, and one connecting the hexes of the inner grid to the hexes of the outer grid). There was one length for the outer equaledge grid. This 6length method is not mathematically accurate, and the model required some coaxing to fit together, resulting in some visually stressed struts.  
5) Here the model is complete and the hemisphere is being deflated 

6) The finished model. Startlingly strong; pulling or pushing any point, the whole structure moves as a single piece. 