Talk:Barth surface

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Sixty-five double points, not fifty?

With respect to the Barth sextic, at first glance, this interesting three-dimensional figure seems to describe a dodecahedron, each of the vertices of which is connected to a corresponding triangular face of an inscribed concentric icosidodecahedron, by twenty tetrahedral shapes. That makes for 20 + 30 = 50 "ordinary double points". Is it possible to visualize how the figure actually includes sixty-five such points, rather than only fifty? Also, the text begs for a link to an article explaining "double point". Rt3368 (talk) 21:40, 27 December 2016 (UTC)

Only 50 of the 65 double points are real. The coordinates of the other 15 involve complex numbers. —David Eppstein (talk) 23:11, 27 December 2016 (UTC)

Thanks for the quick response. I saw that the likely symmetry of the fifteen complex double points must somehow correspond to the lines through the center of the figure that also pass through each pair of opposed vertices of the icosidodecahedron. A search lead me to a confirmation of this in a lucent article written by John Baez at AMS blogs. I went out on a limb and composed a short, informal accounting of the double points. I am a lay person utterly and my factual understanding and language are both eminently assailable. Sadly, 98% of WP's math articles are impenetrable by lay people, so when a beautiful object such as this seems informally describable in English, I count it as a score.

I think I can accurately describe what an ordinary double point is when a curve intersects itself in a plane (a crunode) but a correct definition of a surface intersecting itself in a single point is out of my wheelhouse.Rt3368 (talk) 10:55, 28 December 2016 (UTC)