These 10,000 hexagons are inhabitants of Hexworld, where the ruling class are the rounded hexagons (Rounds). They have ruled for over a thousand years, over the sharp-edged working-class hexagons (Sharps). The Rounds feel they are superior as they have the same shape as the outer wall of Hexworld, an ancient stone wall that has been around for as long as the records go back.

In recent years, some hexagons have been born with a mutant gene. This gives them both sharp and round edges. The Rounds, seeing this as a threat to their rule, have been searching out these mutants and banishing them to the Outlands. These are harsh barren wastelands where no one returns from and are rumoured to have horrible monsters with irregular geometry.