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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
It is an asymmetrical oval slice of toroid, tilted out of the ground towards the south to catch the sun's heat.
When stretched at fixed displacement, the toroid undergoes a transition from an ellipse to a tadpole regime.
The geometry of the house is based on that of an elliptical toroid.
The toroid adds additional optical power in the vertical direction to bring the two focal planes together.
We then look at the case of a toroid compressed in the plane of the toroid.
The roof shapes are engaging, seemingly free-form, but are actually segments of a toroid.

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