Wasn't it hermans who wrote:
>Anton Sherwood schreef:
>> hermans wrote:
>> 
>>> Barth's SEXTIC is a surface with 65 double points. It's interesting to 
>>> know that 20 of these double points are the vertices of a regular 
>>> dodecahedron and 30 other double points are the midpoints of the edges 
>>> of another regular dodecahedron. 
>> 
>> 
>> And the other five?
>> 
>That's an interesting question, but I can't give the answer. Perhaps 
>somebody else can help.
>As mentioned in a link on my page concerning this surface, Barth's 
>sextic is a 6th degree surface that has the maximum number of double 
>points (65) a 6th degree surface can have.

I spent a while trying to imagine how such a symmetric object could have
an extra 5 points that formed any sort of symmetrical pattern, and
became pretty well convinced that it can't happen.

Then I noticed that 65 - 30 - 20 = 15.

However, I still can't find them, and can't think of any symmetrical
patterns of 15 points that don't have a point at the centre.

-- 
Mike Williams
Gentleman of Leisure

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