Veit> On Jan 7, 2014, at 11:11 AM, "W. Edwin Clark" <wclark@mail.usf.edu> wrote: I see one that has n-fold symmetry for all n. So there is no smallest n not made. By "n-fold symmetry" I meant that the maximal symmetry group is C_n or D_n. C_n Hubcaps have to be made in two forms, one for each side of the car. <Veit I never thought of that. But have the carmakers? Zero for 2 in the Tastebuds parking lot: C_10 (modulo lugs) http://gosper.org/IMG_0174.JPG http://gosper.org/IMG_0175.JPG C_7 http://gosper.org/IMG_0176.JPG http://gosper.org/IMG_0177.JPG WEC>I guess you mean has symmetry group C_n or D_n. --rwg NeilB just now reports having Googled hubcap images with either C_n or D_n for every 2≤n≤22. (The TereX Titan has 38 (huge) lugs, but only D_2.) Gary Antonick has run NeilB's and my Lissajous illusions in http://wordplay.blogs.nytimes.com/2014/01/06/2013/?_r=0 <http://wordplay.blogs.nytimes.com/category/Numberplay/> Check the comments at the bottom. Gary and most of the commenters initially mistook these for ordinary spinning dancer illusions.
On Jan 8, 2014, at 7:20 PM, Bill Gosper <billgosper@gmail.com> wrote:
C_n Hubcaps have to be made in two forms, one for each side of the car.
Okay, so I was wrong about that. But you'd think it would be so for "racemic" cars, like Ferraris and Lamborghinis.
<Veit
I never thought of that. But have the carmakers? Zero for 2 in the Tastebuds parking lot:
C_10 (modulo lugs) http://gosper.org/IMG_0174.JPG http://gosper.org/IMG_0175.JPG C_7 http://gosper.org/IMG_0176.JPG http://gosper.org/IMG_0177.JPG
WEC>I guess you mean has symmetry group C_n or D_n.
--rwg NeilB just now reports having Googled hubcap images with
either C_n or D_n for every 2≤n≤22. (The TereX Titan has
38 (huge) lugs, but only D_2.)
I'm stunned: there are 17-gons rolling on our highways??
Well, my example was the '90-91 Honda Accord, but it has a valve stem, resulting in symmetry group D_2. That said, it seems like this '88-89 Hyundai Excel wheel works: http://www.roadwheels.us/13-88-89-hyundai-excel-17-spoke-replacement-wheel-c... It doesn't even have apparent lug nuts! --Neil Bickford On Wed, Jan 8, 2014 at 5:50 PM, Veit Elser <ve10@cornell.edu> wrote:
On Jan 8, 2014, at 7:20 PM, Bill Gosper <billgosper@gmail.com> wrote:
C_n Hubcaps have to be made in two forms, one for each side of the car.
Okay, so I was wrong about that. But you'd think it would be so for "racemic" cars, like Ferraris and Lamborghinis.
<Veit
I never thought of that. But have the carmakers? Zero for 2 in the Tastebuds parking lot:
C_10 (modulo lugs) http://gosper.org/IMG_0174.JPG http://gosper.org/IMG_0175.JPG C_7 http://gosper.org/IMG_0176.JPG http://gosper.org/IMG_0177.JPG
WEC>I guess you mean has symmetry group C_n or D_n.
--rwg NeilB just now reports having Googled hubcap images with
either C_n or D_n for every 2≤n≤22. (The TereX Titan has
38 (huge) lugs, but only D_2.)
I'm stunned: there are 17-gons rolling on our highways??
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Veit Elser