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What is a torus?

What is a torus? Here are some definitions.

Noun
  1. (topology) A topological space which is a product of two circles.
  2. (mathematics) The standard representation of such a space in 3-dimensional Euclidean space: a shape consisting of a ring with a circular cross-section: the shape of an inner tube or hollow doughnut.
  3. (topology, in combination, n-torus, 4-torus, etc.) The product of the specified number of circles.
  4. (architecture) A molding which projects at the base of a column and above the plinth.
  5. (botany) The end of the peduncle or flower stalk to which the floral parts (or in the Asteraceae, the florets of a flower head) are attached; receptacle, thalamus.
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To avoid edge effects, the lattice is represented on a circle for a one-dimensional model or a torus for a two-dimensional model.
It is endlessly turning upon itself, a torus, a doughnut, spinning on the axis of the circular cylinder that is the doughnut.
Joining the remaining pair of sides turns the cylinder into a doughnut, or torus.
The defense platform was a torus with three large solar panel arrays extending out from it with 120 degrees between them.
It therefore has a different topology from the torus of fig. 4, which was be deformed into a mug with only one handle.
Hence the results presented for the torus will have general relevance for vestibular channels.

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