Boys Surface

Boy's surface

Boy’s surface is an immersion of the real projective plane in three-dimensional space, discovered in 1901 by Werner Boy on a mission to disprove that the projective plane could be immersed in 3D space.

Rob Kusner and Robert Bryant has devised the following parametrization of the surface:
\[% \begin{split} g_1 = & -\frac{3}{2}\operatorname{Im} \left[ \frac{w(1-w^4)}{w^6 + \sqrt{5}w^3-1} \right] \\ g_2 = & -\frac{3}{2}\operatorname{Re} \left[ \frac{w(1+w^4)}{w^6 + \sqrt{5}w^3-1} \right] \\ g_3 = & \operatorname{Im} \left[ \frac{w(1+w^6)}{w^6 + \sqrt{5}w^3-1} \right] - \frac{1}{2}\\ \end{split}% \]
where \(g=g_1^2+g_2^2+g_3^2\) and \(|z| \leq 1\).

Production details

All prints are produced on a inkjet printer on Innova’s IFA-22 paper:

  • 315 g/m2
  • Soft textured
  • 100% cotton
  • Natural white
  • Acid and lignin free

Prints are currently only available in the DIN A4 format. If you are interested in other formats, please let me know.