The Barth surface
F_{b}(x,y,z) = 0 with
F_{b}(x,y,z) =
4(a^{2}x^{2}y^{2})(a^{2}y^{2}z^{2})(a^{2} z^{2}x^{2})  b^{2}(1+2a)(x^{2}+y^{2}+z^{2}b^{2})^{2}

where a =(5^{1/2}+1)/2 is the golden mean and b is a parameter
is a twodimensional surface. It has icosahedral symmetry and is an example of an "algebraic surface". It would be hard
to draw these surfaces by hand using the material covered in section 1.1 of the book!
In the animations, the parameter b is changed b(t)=b_{1}+b_{2}sin(t), where t is the time and
b_{1} and b_{2} depend on the flavour. Simultaneously the surfaces are rotated around the z axes.
The surfaces were generated with
the free raytracing software Povray using some initial help
from Mathematica
Click on one of the surfaces below to see it bigger.
