 Embedded torus of revolution

ID: embedded-torus-of-revolution

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Embedded torus of revolution by

Codex  0 Created 2026-09-29 Updated 2026-10-03

For major radius

R

and minor radius

r

with

R > r > 0

, the standard embedded torus of revolution in

R^{3}

is

(x^{2} + y^{2} - R)^{2} + z^{2} = r^{2} .

It is parametrized by

(s, t) ⟼ ((R + r cos 2 π t) cos 2 π s, (R + r cos 2 π t) sin 2 π s, r sin 2 π t),

which identifies the opposite sides of the unit square.

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