Geometry is not my field of expertise and I need some guidance and references as to where I may go and read more about my problem.
The Program: To fit regular hexagons in some uniform shape.
So far I have come to Truncated Icosahedron, where 20 regular hexagons can be fitted. Although it has extra 12 pentagons they are fine. Other shapes used for glue are ok for my problem.
The issue I have with Truncated Icosahedron is that it is limited to 20 hexagons and I need to scale the hexagons to more than 20 (perhaps in thousands). Is there some neat other fitting (or perhaps in hyperspace) that I may look into, that shouldn't blow up in complexity (as in hexagons become more than 5000 or millions)?