[Howto]: Berlingot (+ also Hourglass and Water Drop)

[Eric]

Now you have the first bulb of the 255-hourglass.

Add a tripod on top. And there you get the 132-water drop.

Rotate the shape on the side.

[Eric]

Now choose a triangle just below the pink vertex. It must be surrounded by 3 pentagons!

Proceed the same way as for the pink vertex to build the blue vertex.

And again for the 3rd vertex.

[Eric]

And for the 4th one.

[Eric]

And there it is!

[Eric]

Ooh, this is really really clever Eric!
Compliments!

Thank you very much Peter

Now I'd like to find a way to twist the vertices even more (an extra notch or two), but I can't figure out how to do this yet.

If you look closely, the edge that starts from each vertex (underlined by my colored rods here) does not go towards the opposite vertex (otherwise it would be a simple tetrahedral pyramid), but reaches the edge that starts from it, 3 rods below. What would it look like if it was 4 or 5 rods down? Probably an even more rounded shape?

There are clues in there, but it remains to be worked on.

If you look at this example (which I found yesterday while searching the forum), the tetrahedron is less twisted since the edge starting from one vertex reaches at one rod under the next vertex. And it's not a question of overall dimension of the construction, since my medium-sized berlingot (a little shorter) is twisted 2 rods under the next vertex.

If anyone has an idea about that, I'm a taker.