Editing Boy's surface (section)

===Property of Bryant–Kusner parametrization===
{{Wikibooks|Famous Theorems of Mathematics|Boy's surface}}
If ''w'' is replaced by the negative reciprocal of its [[complex conjugate]], <math display="inline">-{1 \over w^\star},</math> then the functions ''g''<sub>1</sub>, ''g''<sub>2</sub>, and ''g''<sub>3</sub> of ''w'' are left unchanged.

By replacing {{math|''w''}} in terms of its real and imaginary parts {{math|1=''w'' = ''s'' + ''it''}}, and expanding resulting parameterization, one may obtain a parameterization of Boy's surface in terms of [[rational function]]s of {{math|''s''}} and {{math|''t''}}. This shows that Boy's surface is not only an [[algebraic surface]], but even a [[rational surface]]. The remark of the preceding paragraph shows that the [[generic fiber]] of this parameterization consists of two points (that is that almost every point of Boy's surface may be obtained by two parameters values).