I gurgled:> Yow, there are totient(n)/2 of these for every star polygon(n/d), i.e.
(totient(n)/2)^2 for every n. The nine for n=7: www.tweedledum.com/rwg/sphericons7.PNG . No, for even n there are more, because there are two kinds of mirror symmetry.
Oops, those other kind aren't one-piece! On 8/23/10, Bill Gosper <billgosper@gmail.com> wrote:
YOW, http://www.flickr.com/photos/sbprzd/3138091584/in/set-72157604502314691/, http://www.flickr.com/photos/sbprzd/3074973521/in/set-72157604502314691/ is the symmetrical one I was about to waste hours unpeeling! It looks a bit too cylindrical to stretch a horsehide sphere over. Have you tried the (heptagonal) third image in http://www.tweedledum.com/rwg/sphericons7.PNG, or better(?) yet, http://www.tweedledum.com/rwg/sphericon6.png , which has no flat face?
Oops, that unwinds into a closed belt (of significantly larger diameter). What a strange way to peel a tangerine. This could still work for baseballs if we can breed animals, e.g., Naugas, with cylindrical legs of the correct diameter.
--rwg
I guess "rind" is a better name than "sphericon". Especially if we make them out of papyrus.
Seb>And here is a version with a spherical image printed on it:
http://www.flickr.com/photos/sbprzd/3135520252/in/set-72157604502314691/
and they can indeed be printed and glued: http://www.flickr.com/photos/sbprzd/3074973521/in/set-72157604502314691/
Cheers,
Seb