jedidia
shoemaker without legs
I was just wondering... I got this algorithm from the net that creates a geodesic sphere by subdividing an Icosahedron, making two new triangles at every edge. This works flawlessly and has already been adapted to my needs, but now I'm wondering about something.
What I need in the end is the dual of the sphere. With this algorithm, the number of tiles in the dual will roughly tripple (*3 - 4 to be exact) for every subdivision step. As far as I can see, there's really not many other options to subdivide a sphere this way, but I am not certain.
While it is perfectly clear that a sphere cannot be tiled with an arbitrary number of equal triangles, I am wondering whether the currently possible number of triangles are a limitation of the mathematics of the sphere itself or just a limitation of this specific creation method.
I would not mind having some intermiediate sizes to what I have currently (32, 92, 272, 812, 2432 and 7292 tiles in the dual), and while I think that's impossible, I wanted to make sure of that before going on.
What I need in the end is the dual of the sphere. With this algorithm, the number of tiles in the dual will roughly tripple (*3 - 4 to be exact) for every subdivision step. As far as I can see, there's really not many other options to subdivide a sphere this way, but I am not certain.
While it is perfectly clear that a sphere cannot be tiled with an arbitrary number of equal triangles, I am wondering whether the currently possible number of triangles are a limitation of the mathematics of the sphere itself or just a limitation of this specific creation method.
I would not mind having some intermiediate sizes to what I have currently (32, 92, 272, 812, 2432 and 7292 tiles in the dual), and while I think that's impossible, I wanted to make sure of that before going on.
