Comments on: the buckyball symmetries http://www.neverendingbooks.org/index.php/the-buckyball-symmetries.html lieven le bruyn's blog Fri, 20 Jan 2012 16:50:41 +0100 hourly 1 http://wordpress.org/?v=3.3.1 By: D. Eppstein http://www.neverendingbooks.org/index.php/the-buckyball-symmetries.html/comment-page-1#comment-5840 D. Eppstein Mon, 30 Jun 2008 21:06:05 +0000 http://www.neverendingbooks.org/?p=435#comment-5840 <p>Er. All my angle brackets got eaten. The CCC presentation should be <r,f | r^3, f^2, (rfr^{-1}f)^2> and the S4 presentation should be <a,b | a^3, b^2, (ab)^4>. Sorry about that.</p> Er. All my angle brackets got eaten. The CCC presentation should be <r,f | r^3, f^2, (rfr^{-1}f)^2> and the S4 presentation should be <a,b | a^3, b^2, (ab)^4>. Sorry about that.

]]> By: D. Eppstein http://www.neverendingbooks.org/index.php/the-buckyball-symmetries.html/comment-page-1#comment-5839 D. Eppstein Mon, 30 Jun 2008 21:04:32 +0000 http://www.neverendingbooks.org/?p=435#comment-5839 <p>The truncated cube is also the Cayley graph of the group . This is different from its presentation as the Cayley graph of S4, <a>. I imagine the same phenomenon of being the Cayley graph for multiple groups occurs for others of the examples you list.</p> <p>More generally the truncated cube is an instance (with k=3) of the <a href="http://en.wikipedia.org/wiki/Cube-connected_cycles" rel="nofollow">cube-connected cycles</a>, the Cayley graph of a group that acts on strings of k bits by flipping bits and cyclically permuting them.</p> The truncated cube is also the Cayley graph of the group . This is different from its presentation as the Cayley graph of S4, . I imagine the same phenomenon of being the Cayley graph for multiple groups occurs for others of the examples you list.

More generally the truncated cube is an instance (with k=3) of the cube-connected cycles, the Cayley graph of a group that acts on strings of k bits by flipping bits and cyclically permuting them.

]]> By: Florin http://www.neverendingbooks.org/index.php/the-buckyball-symmetries.html/comment-page-1#comment-5837 Florin Mon, 30 Jun 2008 17:37:14 +0000 http://www.neverendingbooks.org/?p=435#comment-5837 <p>Not this time indeed. Congratulations, Spain!</p> Not this time indeed. Congratulations, Spain!

]]> By: javier http://www.neverendingbooks.org/index.php/the-buckyball-symmetries.html/comment-page-1#comment-5836 javier Mon, 30 Jun 2008 14:52:55 +0000 http://www.neverendingbooks.org/?p=435#comment-5836 <blockquote> “Football is a game for 22 people that run around, play the ball, and one referee who makes a slew of mistakes, <b>and in the end Germany always wins</b>.” </blockquote> <p>Not this time! :-D</p>

“Football is a game for 22 people that run around, play the ball, and one referee who makes a slew of mistakes, and in the end Germany always wins.”

Not this time! :-D

]]> By: lieven http://www.neverendingbooks.org/index.php/the-buckyball-symmetries.html/comment-page-1#comment-5834 lieven Sun, 29 Jun 2008 10:05:04 +0000 http://www.neverendingbooks.org/?p=435#comment-5834 <p>I dont think I'll be divulging state secrets by setting up this link to the paper <a href="http://www.neverendingbooks.org/DATA/biplanesingerman.pdf" rel="nofollow">From biplanes to the Klein quartic and the Buckyball</a> by Pablo Martin and David Singerman. Note however that this may be a preliminary version, so if you want to use it please contact <a href="http://www.personal.soton.ac.uk/ds1/" rel="nofollow">David Singerman</a> to check the current state of affairs.</p> I dont think I’ll be divulging state secrets by setting up this link to the paper From biplanes to the Klein quartic and the Buckyball by Pablo Martin and David Singerman. Note however that this may be a preliminary version, so if you want to use it please contact David Singerman to check the current state of affairs.

]]> By: Kea http://www.neverendingbooks.org/index.php/the-buckyball-symmetries.html/comment-page-1#comment-5833 Kea Sat, 28 Jun 2008 19:23:38 +0000 http://www.neverendingbooks.org/?p=435#comment-5833 <p>The buckyball curve! Cool! Is there a link to the paper somewhere?</p> The buckyball curve! Cool! Is there a link to the paper somewhere?

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