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What is a toroid?

What is a toroid? Here are some definitions.

Noun
  1. (mathematics) A surface generated by a closed curve (especially a circle) rotating about, but not intersecting or containing, an axis in its own plane.
  2. A ring-shaped object whose surface is a torus.
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Examples
The toroid adds additional optical power in the vertical direction to bring the two focal planes together.
When stretched at fixed displacement, the toroid undergoes a transition from an ellipse to a tadpole regime.
We then look at the case of a toroid compressed in the plane of the toroid.
It is an asymmetrical oval slice of toroid, tilted out of the ground towards the south to catch the sun's heat.
The roof shapes are engaging, seemingly free-form, but are actually segments of a toroid.
They found that instead of polarization, the new phase creates what the researchers call a toroid moment, which rotates in a circular fashion like a vortex or a tornado.

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