Ok, to start with, please go easy on me - I only have secondary school level maths, and that was 24 years ago.

I'm looking to work out how to evenly distribute points over a sphere.

Specifically 20 points and 24 points.

With the 20 points, I know that a regular icosahedron has 20 faces made of equilateral triangles. But it's not a sphere.

But with the faces all having a centre point equidistant from each corner, I presume that running a line through the centre points to their opposite faces would project out onto the sphere, but would they be equally spaced?

The 24 faces are a bit more problematic.

The 2 most equal designs are the trapezoidal or deltoidal icositetrahedron where each face is kite shaped, or the pentagonal icositetrahedron where each face is pentagonal, but not a regular polygon.

In both of these cases, the centre point of each face is not equidistant from the corners.

Without 3D modelling software, how can I work this out?


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