Chestahedral Star

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.)

Chestahedral Star-1
Chestahedral Star-1- top view

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.

Chestahedral Star-2
Chestahedral Star-2 – alternate view, you can barely discern the convexity
Chestahedral Star-3
Chestahedral Star-3 - bottom view

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.

Chestahedral Star-4
Chestahedral Star-4
Chestahedral Star-5
Chestahedral Star-5

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…

One Comment

  1. Hector ramos

    Seth millers work in chestahdrons designs of chestahedron crosses and stars could be blue prints for cathedrals or buildings he mentioned a chestahedron sphere like epcots sphere chestsphere this could be a blu print for some kind of epcot like chestahedron theme research park with architecture based on the chestahedron Research center on chestapyramid energy .chestapyramid for meditation. Epcot like chestapark eventually a pilgramage place for a religion covenant based on the chestahedron that includes the new mystery center you designed frank imagen a chestaring circular building 1 mile in diameter made of 96 chestahedron with a large chestapyramid in center the size of the greatpyramid it will be a pilgramige sacred are like mecca you could see worshipers going around the chestapyramid 7 times theme park like mecca .jerusalem .

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