Carbon Beauty

In a series of posts on the buckyball trinity, Lieven Le Bruyn gives a link to this paper by P. Martin and D. Singerman on the genus 70 buckyball curve. On page 8 they discuss the familiar Fano geometry of seven points and seven lines, described by a 7 dimensional circulant

1110010
0111001
1011100
0101110
0010111
1001011
1100101

This geometry is embedded in the genus 3 Klein surface. The buckyball curve appears as an embedding space for the $p = 11$ analogue, described by an 11 dimensional circulant

10110100011
11011010001
11101101000
01110110100
00111011010
00011101101
10001110110
01000111011
10100011101
11010001110
01101000111

One guesses that this must somehow be associated to the algebra $E11$, the mathematics of which give the likes of Woit so much confidence that they know more than a lot of very smart string theorists. But in M Theory, we don't care so much about the continuum mathematics, because the physics is actually much simpler than that.