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A helix is a curve in three dimensions. The thread of a screw is a helix, and wire coiled around a rod makes a helix. A spiral staircase is a helix. Some plants, like in the picture, naturally grow into helixes.
The word "coil" is sometimes used to mean a helix and sometimes used to mean a spiral, or sometimes used to mean the act of wrapping something around something else to make a helix or spiral.
The word "coil" is sometimes used to mean a helix and sometimes used to mean a spiral, or sometimes used to mean the act of wrapping something around something else to make a helix or spiral.