According to

http://en.wikipedia.org/wiki/Seifert_surface

every knot or link is the boundary of a compact, connected, and oriented
surface called a Seifert surface.

Recently, I found SeifertView, a Windows application that generates and
displays beautiful representations of such surfaces:

http://www.win.tue.nl/~vanwijk/seifertview/index.htm

Here's a gallery:

http://www.win.tue.nl/~vanwijk/seifertview/knot_gallery.htm

Unfortunately, the source code is not available.  However, the author
mentioned that the program is written in Delphi.  Perhaps the literature
contains a computational recipe we can adapt for Sage.

Anyway, the binary does run on Linux, in emulation:

wine seifertview.exe



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