x_{1} is a torus of genus x_{2} (li; nonnegative integer), having x_{3} (li; nonnegative integer) distinct cusps, and with other properties/characteristics x_{4}, by standard/in sense x_{5}; x_{1} is an x_{2}-fold torus.

The contextless default for x_{3} is probably 0. A coffee mug is a 1-fold torus by the standard of topology but not by the standard of geometry. x_{2} can be only a nonnegative integer or some sort of infinity. See also: cukydjine, where the material properties and realization of the (physical) object matter. x_{2 }= 0, x_{3 }= 1 means that x_{1} is a horn(ed) torus (the cross-section with the two circles has them intersecting at exactly 1 point); x_{0 }= 1, x_{3 }= 2 means that x_{1} is a spindle torus (the cross-section with the two circles has them intersecting at exactly 2 points); x_{2 }= 0, x_{3 }= ro means that x_{1} is a sphere (the cross-section with the two circles has them intersecting at all of their points (which also is uncountably infinitely many) so that they are mutually indistinguishable); x_{2 }= 1, x_{3 }= 0 means that x_{1} is a standard/basic torus (the cross-section with the two circles has them intersecting at exactly 0 points; the result is a classic 'donut' shape).