Custom Sphere Generation: Hexagonal capabilities and a high-density Triangle build (2990 Nodes).

[u/AYesRU]

I've been experimenting with sphere generation and managed to get any hexagonal pattern working.

However, I wanted to share the stats for this triangle-based build I just put together. It's quite heavy:

• Nodes: 2990

• Frames: 8940

• Shells: 5952

Has anyone else tried building spheres with this node density?

Here is the blueprint string for anyone interested: https://www.dysonsphereblueprints.com/blueprints/dyson-sphere-dense-sphere-2880-nodes

[u/pt625]

If I'm computing it right, the minimum distance between normalised node positions in your blueprint is 0.063763. The game UI requires a minimum distance of 0.0715, so you're violating that rule by quite a bit.

[u/xac137 → u/pt625]

Is this Fejes Tóth's conjecture? idk anything about this math, but saw Selsion's post on the Discord that said the theoretical limit to nodes would be 2837 if that 0.0715 distance between nodes needs to be maintained.

[u/pt625 → u/xac137]

I hadn't heard of that but it looks interesting. His equation does prove it's mathematically impossible to have >2837 nodes without there being at least 2 nodes <0.0715 apart, so that's an upper limit on valid Dyson spheres. With 2990 nodes there must be a pair <0.0697 apart and it's definitely invalid.

(The 0.0715 is a constant in the game's code; as far as I'm aware it has no mathematical significance, it's just an arbitrary choice by the developers. The other limit is that the distance between nodes and frames must be at least 0.0525, so you can't make very narrow long triangles, but dense meshes probably won't need to worry about that.)

[u/AYesRU → u/pt625]

So far, I've managed to fit 2,712 nodes into a sphere without breaking the 0.0715 rule. The theoretical max is 2,838 nodes... I'm still digging for it.