I've create this lil sphere from icosahedron using subdivision method. Now i want split it to hexagonal tiles, but i realy don't know how to do this! i've tried to remove every third vertice to create hexagonal gid out of points but in this method i cant triangulate this hexagons. Maybe someone know algorhitm to do this?

CodePudding user response：

A Goldberg sphere is the dual of a geodesic sphere, which you have already constructed.

You can create it by connecting the "center point" of each triangle to the center points of the 3 adjacent triangles. Each vertex in the geodesic sphere will then become a face.

In order to ensure that the resulting faces are all planar, the appropriate definition of a triangle "center point" is just the intersection of the faces at each of its corners. At each corner, construct a plane tangent to the sphere, and then find the intersection of these 3 planes.

Note that the resulting polyhedron will be a tiny bit bigger -- it will enclose the sphere that you're approximating, whereas the geodesic sphere was enclosed by it. Also the resulting hexagons aren't exactly regular, but quite close.