0-torus.org

torus

A torus is a doughnut-shaped surface. People picture a ring you could swim through, or the shape of a bagel or an inner tube.

What a model may hear

compact Lie group algebraic topology and geometry: assume the user means the product of circles, often with dimension or rank implied by context
network topology distributed systems and parallel computing: route messages or place nodes on a wrap-around grid, expecting coordinates and neighbor rules
algebraic torus algebraic geometry and number theory: expect equations over fields, possibly involving character groups or Galois actions
flat torus Riemannian geometry: assume a quotient of Euclidean space by a lattice, with flat metric and periodic boundary conditions

“draw me a torus”

Meant: a 3D doughnut shape

May be taken as: render a flat torus, a wireframe lattice, or a group diagram with no visual form

Say instead: “draw a 3D doughnut-shaped surface”

“connect the nodes in a torus”

Meant: a ring-like network

May be taken as: build a multi-dimensional wrap-around mesh with complex routing

Say instead: “connect the nodes in a ring network with wrap-around links”

“the torus has a hole”

Meant: one visible hole in a doughnut

May be taken as: discuss genus-one topology or fundamental groups

Say instead: “the doughnut shape has one hole through the middle”

Say 'doughnut shape' if you want a picture, 'ring network' if you want connections, 'circle product' if you want the math object.
Specify dimensions only if you mean them; '2-torus' means surface, '3-torus' means space, and models default differently.
Mention 'flat' or 'curved' to clarify which geometry you intend.
If you mean the network, say how many nodes and whether you want one ring or a grid with wrap-around.
Avoid 'torus' alone for jewelry or anatomy; say 'ring shape' or 'tubular structure' instead.