I’ve been curious as to how you can develop a hexagon-tiled sphere (with pentagons) similar to this:

I’m developing this for a prototype that can be compared to a puzzle game, so the hexagons must be dynamic and capable of moving around the sphere. The problem is, I have no idea how to do this in terms of math and programming.

I greatly appreciate anyone taking the time to explain the concepts required for this prototype. Thank you.

So, you really can’t have a sphere like shape that is made of only hexagons.

Furthermore, polyhedrons don’t always scale easily. There are limitations when you subdivide the face of a polyhedron.

But you’re in luck, and it’s also why hexagons are used.

There is a solid called the ‘Dodecahedron’, you may know this as the 12 sided die. You can create a ring around the pentagons out of hexagons. This creates an even more spherical shape as you add more and more rings around that. Making the pentagons the control points of this spherical like polyhedron.

You can actually see this in that video. I have it paused around the 17-18 second mark, and right in the middle of the screen you’ll see one of the pentagons. There’s 12 in total around the entire sphere… you can see others if you continue watching.

You will want to research the math behind geodesic domes, primarily those based on dodecahedrons using hexagonal rings.

Yes, I’ve tried, I seem to just get lost with the math that I find on various places. Do you know of any good source? The main problem is I couldn’t find anything specific (and I’m not that great at math so don’t expect me to just derive something, lol).