The three different classes of standard tori arise from the three possible relative sizes of
corresponds to the ring
torus shown above,
corresponds to the horn torus which touches itself
at the point (0, 0, 0), and corresponds to a to a self-intersectingspindle torus (Pinkall 1986, pp. 30-31).
The unqualified term "torus" is generally taken to refer to a ring
The standard tori and their inversions are cyclides.