Hexagonal geodesic map

Hello,

I don't find on the web the mathematic formule or routine for know the hexagones 3d position and rotation for this type of grid (is an icosahedron dual ?) :

My 0;0;0 position would be the center of the map, and i would like choose the size between 2 pentagons (If I understood correctly, there are always 12 pentagons), like that :

I specify, I have an hexagon mesh, and I doesn't want the method for build the mesh of the grid (On the web, I found only this type of solution). I want to know only the position and rotation of one of the hexagone, with a id.

Schematic example of what I want :

 #define PENTAGONS_NUMBER 12
 
 buildMap(10);
 
 void buildMap(int _size)
 {
    int numberHexagons = computeNumberOfHexagons(_size);
 
    for(int i = 0; i < numberHexagons; i++)
    {
       GameObject go = Instantiate(prefabHexagon, getHexagonPosition(i), getHexagonRotation(i)) as GameObject;
    }
 }

So, can you help me for find (or if you know, give) the routine/formule/explanation for the shematics functions computeNumberOfHexagons(), getHexagonPosition() and getHexagonRotation() ?

Thanking you ! :)