Here are two images of the same Sonobe construction. What is the underlying geometry?
Keep reading for a few hints.
Hint #1: there are 90 units in the construction. Of these, 60 are purple and 30 are grey. (D would like to note that this color choice was her suggestion.) Also, all the units of the same color are interchangeable, in the sense that there is some rotation of the polyhedron that moves a given unit to the position of any other unit of the same color but leaves the overall object looking the same.
Hint #3: I made a twin to the polyhedron from the same number of units connected in the same way. The difference is that the twin was made “inside-out,” so the pockets of the individual Sonobe units are on the inside, rather than the outside. The visual effect is that the little triangular pyramids that usually point outwards instead point inside the polyhedron. Also, the “ribs” of the individual units are readily visible.