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A regular hexagon with one vertex at the origin, and a side along the x-axis and of length s has vertices at:

(0, 0)

(s, 0)

(1.5*s, 0.5*s*√3)

(s, s*√3)

(0, s*√3)

(-0.5*s, s*√3)

Since you now have both endpoints of each line segment, their equations are easy to find.

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