Hex

hex, n. a single hexagonally-shaped space or area on a hex mat; used to represent the space occupied by a single unit or character, and to measure distance, line-of-sight, direction of travel, etc. Pl. hexes. See hex mat, hex paper. [GJ1]
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Addendum: Another one of those signals that one is a paleogamer (or who's played too much Battletech) is the habit of calling any spaces on modern battlemats as hexes, whether they're printed with hexes or squares.