At Truro, MA on Cape Cod there is an old dew (distant early warning) radar dome now used by the FAA which has a skin without any triangles in it. Besides the regular pentagons there are unique elongated irregular hexagons.
I have found a few photos of other domes like this on the Internet. To see a couple of these images just do a GOOGLE Image search for "Radar Dome Bergen". However, these pictures do not show the overall pattern especially well.
Besides the icosahedral placement of the regular pentagons, just what is the arrangement of these irregular hexagons?
The irregular hexagons appear to have a "twisting feature" in their placement. Is there any similarity relationship here to that of the jitterbug transformation for a cubeoctahedron?