I've found it's easy enough to fake, using a bit of maths.
Create sphere. Then Triangulate (Polygons > Mesh > Triangulate.)
Then switch to edit vertex mode, and grab the vertexes on each vertical layer and rotate them around 'en masse'.
The angles you rotate them depend on the number of sub-divs you originally used to create the sphere. I used 12 sub-divs (in other words 12 facets to make up the circumference) of my sphere, so the angle of each polygon was 360/12 = 30. I only wanted to rotate the layers by half a polygon so I divided this by two = 15º, which is what I used for the step-size.
Left the top layer alone, then grabbed and rotated the following layer by 15º, then the third layer by 30º, the fourth layer by 45º, etc...
Took all of 30 seconds to do.
I was wrong in my original assumption that it somehow used less polygons. It uses the same, just in a different arrangement. My error was when you triangulate the sphere you can see the polygons through the back at the same time, making it look like each trapezoid was split into four triangles and not just two.