Having just made the chestahedron template, I thought I’d make a few and see how it went. I noticed that six chestahedra fit perfectly together in a star pattern:
(Click any image for larger version.)
Although the form seems to fit flush with the table surface, it actually forms a concave curve, because the six chestahedra angle outward from the center point. This made me wonder: “What is that curve? What if it could be extended?”
I made a few more chestahedra and quickly saw that indeed the curve could be continued quite easily. It was apparent, because of the nature of the equilateral triangular base of the chestahedron, that a three-fold symmetry was at work. The concave surface was made of six triangles that formed a concave hexagon, and the curve could be continued in any direction. I wanted to know if the curve, which obviously formed a circle, would actually meet itself in a way that all the forms fit perfectly together. Perhaps the curve necessitated by the hexagonal tiling was not able to be closed with an integer number of chestahedra.
I did not know how many chestahedra would be needed to test this theory, but based on the curve formed by six together it seemed like it wouldn’t be so many as to be impractical. It turns out that 96 chestahedra are needed to form what I call the chestahedral ring.
The form was very beautiful and sculpturally intriguing. The curve of the ring is necessitated by the way the individual chestahedra interlock; there is only one chestahedral ring when configured in this way. The forms are made out of #60 card stock and scotch tape. The equilateral triangles have a side length of approximately three inches, and this makes the final inner diameter of the form approximately 22 inches.
Obviously the form could have extended in any other direction; it seemed that in fact that this particular tiling suggested a complete sphere, the chestahedral sphere. Triangles easily tile the surface of a sphere, as Buckminster Fuller discovered with the geodesic domes. The chestahedral sphere is a form of geodesic dome on the inside, but what is unique about this form is its three-dimensionality. Each of the three side triangles on an individual chestahedra adjoins others from neighboring chestahedra, giving the whole form a particular necessary self-integration that works with the full volume of space. Contrast this with the famous geodesic sphere of the Epcot Center, where the triangular elements of the dome are simply raised at their center point into flattened tetrahedra, which have no structural relevance. The chestahedral sphere is integrated structurally in three dimensions. This all flows naturally and necessarily from the specific form of the chestahedron itself. The chestahedron, which is made only of straight lines, still has as a part of its nature a curve.
It was obvious that I would have to make more chestahedra…