Message #1644

From: Andrey <andreyastrelin@yahoo.com>
Subject: Re: some stained glass
Date: Tue, 03 May 2011 08:24:46 -0000

Yes, in vertex turning {3,n} you don’t care about "corners" orientation, but "centers" orientation is significant there. So you just trade one problem to another. Orientation of centers is not a problem for commutator-based algorithms (in 2D puzzles), but if you solve this puzzle by growing of solved area, you should select center orientation before you "attach" the first 2C piece to it.
So I’m not sure that {3,7} is more easy than {7,3} - they are almost the same. But there are too many colors in {3,7} - piece search may be a problem.

Andrey

— In 4D_Cubing@yahoogroups.com, "schuma" <mananself@…> wrote:
>
> The {3,4} counterpart (Gelatinbrain 4.2.1) is more well known, usually called Trajber’s Octahedron. It is now a mass produced cheap puzzle. It’s just a shape mod and color variation of the common 3x3x3. In my opinion, it’s even easier than 3x3x3 because you don’t have to worry about the orientation of corners. The 4x4x4 analog is also mass produced. <http://shop.ebay.com/i.html?_from=R40&_trksid=m570&_nkw=trajber&_sacat=See-All-Categories>
>
> So I believe this vertex turning {3,7} is easier than the current Klein’s quartic. (certainly much easier than the face turning {3,7})
>
> Nan
>
> — In 4D_Cubing@yahoogroups.com, Roice Nelson <roice3@> wrote:
> >
> > Yep, it is based on the {3,7} tiling, and has 56 faces. It is also
> > noteworthy because the picture is of a vertex-turning puzzle rather than a
> > face-turning one (the centers of the slicing circles coincide with the
> > vertices). So I suppose this could be considered a hyperbolic analogue to
> > gelatinbrain’s 2.2.2. It should be a much more pleasant puzzle to solve
> > than the face-turning {3,7} will be.
> >
> > Melinda, the texture approach in my recent MagicTile v2 coding has been
> > working out fantastically, and one great thing about that is I should be
> > able to map it to an IRP representation at some point without a great deal
> > of effort :D
> >
> > seeya,
> > Roice
> >
> > On Mon, May 2, 2011 at 9:51 PM, Melinda Green <melinda@>wrote:
> >
> > > That’s my guess too. Here is an undistorted model I built a long time
> > > ago, and in cross-eyed stereo to boot:
> > >
> > > http://superliminal.com/geometry/3_7st.jpg
> > >
> > > I would sure love to solve it in this form. It may not even be that hard
> > > to implement using a single dynamic texture mapped onto this surface.
> > >
> > > -Melinda
> > >
> > > On 5/2/2011 7:43 PM, schuma wrote:
> > > > Is it the dual of Klein’s quartic?
> > > >
> > > > — In 4D_Cubing@yahoogroups.com, Roice Nelson<roice3@> wrote:
> > > >> Here’s another puzzle quiz to throw out there, and shouldn’t be too hard
> > > :)
> > > >> Can you tell what it is?
> > > >>
> > > >> http://www.gravitation3d.com/magictile/pics/stained_glass.png
> > >
> > >
> > > ————————————
> > >
> > > Yahoo! Groups Links
> > >
> > >
> > >
> > >
> >
>