The symmetry group of the icosahedron is a subgroup of . The bipolyhedral group is the image of in . It has exactly two invariants of degree 12:
Now let .
This surface is invariant under the bipolyhedral group and has exactly 600 nodes. It was discovered by A. Sarti (Erlangen) in 1999.
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Institute of mathematics of the Gutenberg University of Mainz, Germany