Rotating Barth's Surface

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This shows (the real coordinate points of) Barth's surface drawn with the symbolic manipulation program Mathematica. Barth's surface is known as a sextic surface in the complex three dimensional projective space with sixty five double points.
Viewing this animation, we notice that a dodecahedron is hidden in the picture. We could never imagine the dodecahedron only with its defining equation:
We used a special package ImplicitPlot3D.m by Steven Wilkinson for drawing this picture.

Reference: http://www.math.uni-hamburg.de/home/riemenschneider/barth.html

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