# Boys 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 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.

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