# Algebraic surfaces from here, there, and everywhere

## Nordstrand's weird surface

\[ 25 (x^3 (y+z)+y^3 (x+z)+z^3 (x+y))+ \\ 50 (x^2 y^2+x^2 z^2+y^2 z^2) - \\ 125 (x^2 y z+y^2 x z+z^2 x y) + \\ 60 x y z - 4 (x y+x z+y z) = 0 \]

Printed into neon green ninjaflex in 2015 at Notre Dame on a Taz4. Water-soluble PVA was used as support material. One made.

## The Barth Sextic

\[ 4 (\phi^2 x^2-y^2) (\phi^2 y^2-z^2) (\phi^2 z^2-x^2) - \\ (1+2 \phi) (x^2+y^2+z^2-w^2)^2 w^2 \\ = 0\]

where

\[\phi=\frac{\sqrt{5}+1}{2} \]

and in this view, \(w = 1\).

What a wonderful surface. Maximally singular for a degree 6 surface in \(\mathbb{P}^3\), in terms of double points.

These prints vary widely in scale. The smallest is an earring, about 30mm in diameter, printed in white TPU. The largest is over 200mm in diameter, in Luminous Green PLA plastic. All are printed as one piece on my printers.