@flawr I started by dropping a point in the centre of a square to add 3 Voronoi vertices with one input vertex. And then I just tried breaking up two of the four Voronoi vortices into triangles with one input vertex each. (I tried a few other things that didn't work out though)

@flawr I wonder if it changes once you have at least one finite cell in the Voronoi diagram

still not quite. if you have one input vertex at the origin, and all others on a circle, the radius of the circle doesn't affect the Voronoi diagram (but the cell around the origin is finite)

@MartinEnder I don't agree: If you increase the radius, the edges of the cell move further away, right?

oh duh, of course

it was clearly too late last night

I'm not quite sure, but now I think I have |P_{i+1}| <= 2|P_i|-5 (again using Eulers polyhedron/planar graph formula)

@PhiNotPi 9.00 km/s to leave Earth's gravitational influence, then an extra 8.72 km/s to leave the Sun's gravitational influence. It's harder to get off Earth than it is to leave the Solar System once you're off Earth.

That's a really cool graph.

Hypothetical problem solving time! Let's say you've got a point cloud with lines connecting them in some manner, forming a graph. This point cloud can be in any number of dimensions. Let's say 10. I can draw three of those dimensions on-screen at a time (more properly, the span of any three orthogonal basis vectors). I would like to be able to give the user the ability to rotate these "camera vectors", so to speak, so they can see what the graph looks like along other dimensions.

10 dimensions is too many to give the user direct control over each basis vector. While technically possible, such a solution would be quite unwieldy. So there has to be some other way(s) to give the user the ability to rotate the camera in ways that will reveal potentially interesting structures in the graph.

E.g. select three points, align camera to normal.

Okay, this problem isn't entirely hypothetical. I expect I'll have to solve it in like a month or so for the project I'm working on.