In games and VR we encounter the problem of projecting an image onto a sphere all the time. There are many approaches, from wrapping a plane into a sphere to simply normalizing the vertices of a cube with an image on each face. One of the best ways to do this is to take an icosahedron, tessellate the faces into smaller triangles and then normalize all the vertices of the triangles. This is commonly known as an icosphere. It can be more dificult to "unwrap" but it gives the most even distribution of vertices that a triangle mesh representing a sphere can have.
In games and VR we encounter the problem of projecting an image onto a sphere all the time. There are many approaches, from wrapping a plane into a sphere to simply normalizing the vertices of a cube with an image on each face. One of the best ways to do this is to take an icosahedron, tessellate the faces into smaller triangles and then normalize all the vertices of the triangles. This is commonly known as an icosphere. It can be more dificult to "unwrap" but it gives the most even distribution of vertices that a triangle mesh representing a sphere can have.