When We Build Our Dyson Sphere, Let’s Not Use Enneagonal Antiprisms

Before an undertaking as great as building a Dyson Sphere, it’s a good idea to plan ahead first. This rotating image shows what my plan for an enneagonal-antiprism-based Dyson Sphere looked like, at the hemisphere stage. At this point, the best I could hope for is was three-fold dihedral symmetry.

Augmented 9- Antiprism

I didn’t get what I was hoping for, but only ended up with plain old three-fold polar symmetry, once my Dyson Sphere plan got at far as it could go without the unit enneagonal antiprisms running into each other. Polyhedra-obsessives tend to also be symmetry-obsessives, and this just isn’t good enough for me.

Augmented 9- Antiprism complete

If we filled in the gaps by creating the convex hull of the above complex of enneagonal antiprisms, in order to capture all the sun’s energy (and make our Dyson Sphere harder to see from outside it), here’s what this would look like, in false color (the real thing would be black) — and the convex hull of this Dyson Sphere design, in my opinion, especially when colored by number of sides per face, really reveals how bad an idea it would be to build our Dyson sphere in this way.

Dyson Sphere Convex hull

We could find ourselves laughed out of the Galactic Alliance if we built such a low-order-of-symmetry Dyson Sphere — so, please, don’t do it. On the other hand, please also stay away from geodesic spheres or their duals, the polyhedra which resemble fullerenes, for we certainly don’t want our Dyson Sphere looking like all the rest of them. We need to find something better, before construction begins. Perhaps a snub dodecahedron? But, if we use a chiral polyhedron, how do we decide which enantiomer to use?

[All three images of my not-good-enough Dyson Sphere plan were created using Stella 4d, which you can get for yourself at this website.]

About RobertLovesPi

I go by RobertLovesPi on-line, and am interested in many things. Welcome to my little slice of the Internet. The viewpoints and opinions expressed on this website are my own. They should not be confused with the views of my employer, nor any other organization, nor institution, of any kind.
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One Response to When We Build Our Dyson Sphere, Let’s Not Use Enneagonal Antiprisms

  1. Unfortunately, Euclidean symmetry has limitations of the “granularity” of Dyson Sphere.

    Instead of perfect symmetric approach, you can try not symmetric, but very nice looking Sunflower Arrangement, it has good mathematical equation, which can be found here (https://en.wikipedia.org/wiki/Helianthus_annuus). This arrangement can be also applied to sphere, see here (http://arxiv.org/abs/1304.4060v1).

    Liked by 1 person

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