**Barth's Sextic Surface**

Barth's sextic surface
is the surface determined by the polynomial equation

Φ=(sqrt(5)+1)/2 is the

The following animation shows the part of the surface inside a sphere centered at the origin.

Wolf Barth (1942-2016) was a German mathematician. In April 2017 Thomas Bauer, Klaus Hulek, Slawomir Rams, Alessandra Sarti and Tomasz Szemberg published an article consacrated to his life and work: Wolf Barth 1942-2016.

As is written in this article:

In 1996 he discovered what is now called

20 nodes (the red ones) are the vertices of a regular dodecahedron:

The other real 30 nodes (the green ones) are the vertices of an

An icosidodecahedron can be constructed in the same way starting from a regular icosahedron.

Limiting the surface to the part within the sphere passing through the red nodes, we obtain the following animation:

Barth's sextic surface clipped by an expanding and shrinking sphere:

**Barth's Decic Surface**

Barth's decic surface
is the surface determined by the polynomial equation

+(3+5Φ)(x

Φ=(sqrt(5)+1)/2 is the

Barth's decic surface has 345 singularities, 300 among them are real nodes.

The following animation shows the part of the surface inside a sphere centered at the origin.

Barth's decic surface clipped by an expanding and shrinking sphere:

Barth's decic surface clipped by a sphere passing through a number of equivalent nodes:

As mentioned in "Barth's decic surface", the nodes of the surface are associated with some more sophisticated polyhedra.

Barth's original paper on his sextic and decic surface:

Barth, W:

Journal of Algebraic Geometry,

Herman Serras

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