Consider a curved $2$D truss that will be used as the structural support for a mesh$-$reflector. The

nodes lie in a paraboloid with focal length $f=20m,$ see Figure $4.$ The structure has a projected

diameter $D=20m.$ All bars with the same color, marked as $b_i,$ are identical. Please, note that all

dimensions in Figure $4$ are not to scale, and that none of the triangles are necessarily regular.

The truss has been designed so that the angular defect is the same in all the nodes that are

shared by six faces $($i$.$e$.,$ not including the nodes on the outer perimeter of the truss$).$ Calculate

the lengths of all the bars. Note: you can solve the problem numerically, no need for a closed form

solution.

$($a$)$

Figure $4$: Parabolic truss structure: $($a$)$ Side view, showing the parabolloid surface and only four

bars $($several other bars are not shown$),$ and $($b$)$ projected view.