This minimal surface is the image of the 6-punctured sphere. Since antipodal points of the sphere have the same image in R^3, the surface is also the image of the 3-punctured projective plane. The punctures are so called “planar ends”, which means, the surface looks outside a large ball like three pairwise orthogonal planes. Inversion of this surface in a sphere gives the famous
Boy's Surface.
We show the surface in three parts. The conjugate surface does not have antipodal symmetry.

Polar Cap

Inverted Boy Equator Band

The equator band in the domain starts from the equator and extends in to one hemisphere
until it approaches the three punctures. As for the polar cap, the parts nearest to the
three punctures get strongly expanded and are almost flat. - For the inverted Boy surface
the image of the equator doubles back onto itsself so that this part of the surface
is a Moebius band. _ One can follow the bands more easily in the anaglyph views.

Inverted Boy Equator Conjugate

Inverted Boy Meridians

In the domain we can find 3 meridian bands from pole to pole which do not run through
the punctures. We made them wide enough so that each comes near a
puncture on both hemisspheres. For the inverted Boy surface the neigborhoods of the
two domain poles have the same image: we see only polar one center. The meridian bands have
therefore Moebius strips as images under the surface map. -- On the conjugate surface
one can see how the (images of the) meridian bands go from polar center to polar
center, each coming near a puncture on both hemisspheres.