Surfaces52 of 113
Barth sextic
Wolf Barth, 1994
A surface of degree six with 65 double points, cone-like pinches where two sheets touch. That is the most any sextic can have, a fact proved only in 1997. It is drawn inside a ball, with the icosahedral symmetry of its golden-ratio equation.
4(φ²x² − y²)(φ²y² − z²)(φ²z² − x²) − (1 + 2φ)(x² + y² + z² − 1)² = 0
On mathcurve.com as Sextique de Barth