The Barth surface
Fb(x,y,z) = 0 with
where a =(51/2+1)/2 is the golden mean and b is a parameter
is a two-dimensional 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!
4(a2x2-y2)(a2y2-z2)(a2 z2-x2) - b2(1+2a)(x2+y2+z2-b2)2
In the animations, the parameter b is changed b(t)=b1+b2sin(t), where t is the time and
b1 and b2 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
Click on one of the surfaces below to see it bigger.