Here is my howto of the double-scale Oloid discussed in the Oloid thread in the 'Math-related Geomag discussions' forum.
Feel also free to take a look at my 'Oloid delirium' thread
Let's start.
First, I make 2 pentagonal bipyramids. The blue one is already finished on the photo below. Let's build the white one.
I thought I needed to reinforce the inner structure to help it keep its perfect shape of pentagonal bipyramid (did it in the blue one).
But I realized by testing it with the white one that it was not necessary. Once properly closed, the structure takes its shape, remains rigid and no longer deforms. So I removed the silver rods.
By connecting the free rods of the 1st photo to the corresponding spheres we give the concave shape to the double-scale pentagon