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The symmetry group of the icosahedron
$$`A`_{5}
is a subgroup of
$$`SO(2)`.
The bipolyhedral group $$`I`
is the image of
$$`A`_{5}x`A`_{5}
in $$`SO(4)`. It has exactly two invariants
of degree 12:

Note that

Now let $$`X`_{12}={243
`S`_{12}-22
`Q`_{12}=0}.

This surface is invariant under the bipolyhedral group
$$`I` and
has exactly 600 nodes.
It was discovered by
A. Sarti (Erlangen)
in 1999.

Stephan Endraß Last update: Thursday, 06-Feb-2003 08:53:00 MET

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Home: The algebraic geometry group,

Institute of mathematics
of the Gutenberg University of Mainz, Germany