3d solid identification

Question

Let me try to describe it:
- start with a cylinder or tube
- collapse (squeeze) base of the cylinder until it becomes a segment - rotate 90 degrees along the height axis - collapse (squeeze) other base of the cylinder until it becomes a segment

As circular bases become segments the net you would use to build it is just rectangular.

Thanks

Answer 1

I agree that figure you care about isn't a tetrahedron (the picture in the same question yesterday). I agree that it's an interesting figure. I'm pretty sure it doesn't have a name. Maybe I'm wrong and someone will know the name.

I think that topologically your figure is an orbifold.

Here's an image with one circle flattened: https://www.math.toronto.edu/drorbn/Gallery/Symmetry/Tilings/22S/PlasticBag.html

There's no way to express in purely topological terms the fact that the other flattening is rotated 90 degrees. You need some kind of metric information for that.