I had wanted to see if it was possible to create a seven-fold star from the chestahedron. I tried multiple configurations but none seemed to work. But I did happen to discover an eight-fold star:
(Click any image for a larger version.)
Notice the elegant eight-fold symmetry. The white kite-shaped faces do not lie in a plane, but form a subtly convex curve. Everything seems to meet perfectly. The white star has a sense of calm symmetry, while the eight yellow chestahedra seem as if they are being flung off spirally towards the periphery. The whole shape is also reminiscent of a gear or ratcheting system, even the teeth of a rotating saw blade.
When flipped over, the form is still striking. The white chestahedra form a perfect octagon, and are held apart from each other, touching only along one edge, by the yellow chestahedra, as if pulled by them. The eight most visible white triangular faces seen here form a distinct bowl shape.
These final two views with a different background have a different flavor; the inner, negative space is emphasized, revealing eight pointed stars… more about the stars later.
It is fascinating that the chestahedron, with its seven faces of equal area, yields an eight-fold symmetry in three dimensions. This is not random by any stretch, as continued exploration shows…