A torispherical dome is the surface obtained from the intersection of a spherical cap with a tangent torus, as illustrated above. The
radius of the sphere
is called the "crown radius," and the radius of the torus is called the "knuckle radius." Torispherical
domes are used to construct pressure vessels.

Let
be the distance from the center of the torus to the center
of the torus tube, let be the radius of the torus tube, and let be the height from the base of the dome to the top. Then the
radius of the base is given by . In addition, by elementary geometry, a torispherical
dome satisfies

(1)

so

(2)

The transition from sphere to torus occurs at the critical radius