You can almost draw a congiguous hexagon map on a subdivided icosahedron, if you subdivide each triangle edge in 3 parts on each recursive step. Adjacent triangles will form hexagons.

This will leave 20 pentagons where the vertices of the original icosahedron's vertices were located. The rest of the sphere can be covered with a regular hexagon map for a strategy game.

I've been thinking about "hiding this" in a game design element so the 20 pentagons would be "capitals" or otherwise special tiles in the game. They're nicely equidistant from each other, so it could make a nice and fair map to play on.