Re: [math-fun] The Plumber's Nightmare Graph

Daniel Asimov <dasimov@earthlink.net> wrote:

In case anyone is interested in some context for this:

...

But it has an even more beautiful metric realization M_K given by one homogeneous complex polynomial defined on the complex projective plane CP^2: the polynomial was discovered by Klein and is

X Y^3 + Y Z^3 + Z X^3 = 0

(where CP^2 is defined as the quotient of C^3 - {0} by (X Y Z) ~ (cX cY cZ) for all nonzero c in C). M_K does not have constant curvature, but it is a minimal surface in CP^2.

Thanks, Dan! Jim Propp