Square to Octahedron...

The goal is to build a 'world object', which could be a planet, moon or asteroid depending on size and need. I'll use a '2d' context, so no textures or lighting, but I can get the thing to turn. I will leave the vertices alone for that, just keep track of angles and do the rotation on the projection. As for what I'm projecting, I'm going to create a cube sphere by way of an octahedron. I will generate the octahedron by way of a square subdivided into four quads which in turn are subdivided and folded into a center and corner triangle. The points xyz are i,j and the absolute new york 'street' distance, so that the corners fold away behind the center to the far vertex of my octahedron.
(click in the black box to turn)