Barth surfaces


The Barth surface Fb(x,y,z) = 0 with
Fb(x,y,z) = 4(a2x2-y2)(a2y2-z2)(a2 z2-x2) - b2(1+2a)(x2+y2+z2-b2)2
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!
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 from Mathematica Click on one of the surfaces below to see it bigger.


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