A Schlafly double-six is defined as a collection of six pairs
of skew lines *(P _{i},Q_{i})* in space so
that for each

*i*different from

*j*,

*P*meets

_{i}*Q*; the

_{j}*P*'s do not meet each other and the

_{i}*Q*'s do not meet each other either.

_{j}The construction of such a sextuple has been known since 1858 when Steiner discussed the 27 lines on a cubic surface with ShlĂ¤fli. More history surrounding the 27 lines can be found at the History of Mathematics web site.

Last year, in response to a "coffee-table" conversation at CalTech, I provided a [two-page write-up][shlafly article] on how one can visualise the construction of such a double-six. As "proof of concept", I produced a number of different povray source files which would draw the constructed lines. I then gave a talk based on the write-up in the AIS school at IIT, Chennai in summer 2007.

In December, we had a visit from Etienne Ghys who gave a
wonderful presentation regarding the Lorenz attractor and its
connection to modular knots. He had produced some movies using
`povray`

which neatly illustrated his talk. During
discussions, he persuaded me that it would be nice to have a
movie about the double-six.

The IMSc Seminar Week seemed like a good excuse to work on my
"film debut"! Unfortunately, I under-estimated the amount of time
this would take and almost chickened out. With a little help from
`schroot`

on a faster machine, I was able to create the movie and also present my talk today.

Let me add that I feel more than a bit embarrassed at using
non-free software (`povray`

) to make the movie. I
could have used `blender`

to create the movie but then
the source would be opaque as it would have been "drawn by hand".
The *language* `povray`

is free and the
source for the movie is quite (I
think!) expressive.