If one performs an inversion of this parametrization centered on the triple point, one obtains a complete minimal surface with three ends (that's how this parametrization was discovered naturally). This implies that the Bryant–Kusner parametrization of Boy's surfaces is "optimal" in the sense that it is the "least bent" immersion of a projective plane into three-space.
If one performs an inversion of this parametrization centered on the triple point one obtains a complete minimal surface with three ends (that's how this parametrization was discovered naturally). This implies that the Bryant–Kusner parametrization of Boy's surfaces is "optimal" in the sense that it is the "least bent" immersion of a projective plane into three-space.