Sectors will look something like this, but a little bigger:

Stsrbound_Dust, what you show here would force a great deal of sector overlap between adjacent sectors. It would make a lot of the mathematical aspects of the game difficult, especially of the "what sector am I in" kind.

That being said, the only way I can envision sectors of hexes is as a hex of hexes. After drawing some diagrams on paper it looks to me that a sector with a radius of 12 hex tiles is not a reasonable way to describe the size of a sector. I was unable to draw a regular hexagon containing either a radius or diameter of an even number of regular hexagons. Therefore, the diameter of a sector will always have to be an odd number of hex tiles, and the radius would have to include only half of the center tile.

I think the galaxy map's sector sizes will be best expressed as the number of hexes on a side. This can be done without any resulting overlap between sectors, and should reduce the confusion experienced by the game players. I also think it would make most (definitely not all) of the calculations the programmers must make easier.

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Well, while I was typing up this reply, it appears that Starbound_dust edited his post, completely changing the diagram of a sector he had.