# Message #1963

From: schuma <mananself@gmail.com>

Subject: Re: Another {7,3} puzzle

Date: Wed, 14 Dec 2011 02:28:42 -0000

Hi Roice,

Between the two {4,3} candidates, I like the second one better, because in candidate #1, it’s so hard to see the tiny pieces. Another reason I don’t like the first one is because the face circles seem to be truncated where they touch the edges (because of the width of edges). They look more like octagons. But in candidate #2 they are more circular.

We can also create candidate #3, which is basically #2, except the face circles are much smaller so that they are tangent to the vertex circles. This candidate should be a direct analog of {5,3}, {6,3}, and {7,3}: face circles tangent to vertex circles; edge circles tangent to each other.

Gelatinbrain also added the FEV {4,3} in his applet, as 3.7.10. You can find a screenshot here:

<https://picasaweb.google.com/lh/photo/aGFi-p2vU57a_WS42KZNddMTjNZETYmyPJy0liipFm0?feat=directlink>

He defines the edge circles in a different way that so that they pass the face centers. In none of our candidates we have this property. In GB 3.7.10 no piece is too small.

So among the candidates I prefer #3, which should also be the easiest to solve. Then #2.

Nan

— In 4D_Cubing@yahoogroups.com, Roice Nelson <roice3@…> wrote:

>

> On Tue, Dec 13, 2011 at 12:23 AM, schuma wrote:

>

> > Roice, thanks for making the beautiful {6,3} and {5,3}!

>

>

> You’re welcome :) I’m glad the work I did to make things configurable is

> paying off a bit now. These both only took only a few minutes to

> configure. I think I’ll send an email soon describing how to do this.

>

>

> > It’s an optical illusion that the face circle appears larger. I think it’s

> > because of the hexagons, and the fact that the face circle is one color

> > whereas the others are filled by two or three colors.

>

>

> The optical illusion got me too! A consequence of your observation is that

> all the small pieces are now the same size. It would therefore be possible

> to extend this puzzle so that edges could twist through 1/6th a turn

> instead of 1/2 turn. Such twists could end up locking adjacent vertex

> twists, but this would extend the orbits of the small pieces (any of them

> could go to any other). But honestly, the thought of trying to code this

> extension scares me - it’s nice to not have to worry about tracking things

> like locked twists.

>

>

> > (2) In {5,3}, if the circles are perfect circles, there should be some

> > tiny pieces. Am I right? One can make the vertex circles tangent to each

> > other, and then make the face circles the right size to be tangent to the

> > vertex circles. But when he/she adds the edge circles, these circles not

> > necessarily pass through the tangent points. By zooming it in, it seems

> > like the adjacent edge circles intersect within the face circles by a

> > little bit. If it’s true, I appreciate eliminating the tiny pieces to keep

> > this puzzle neat.

>

>

> Wow, this I did not expect, but you are right! Since the {5,3} doesn’t fit

> together perfectly, I immediately suspected the {7,3} does not either, and

> sure enough, that is true as well. In both cases, the thickness I used for

> the slices had the effect of removing those tiny pieces (the slice

> thickness is configurable, so this doesn’t have to be the case). I like

> them better without the tiny pieces as well, but this diminishes the

> elegance of these puzzles a bit, excepting the {6,3} of course.

>

> > (3) I noticed the geometric issue of {5,3} because I was trying to draw

> > the corresponding cube puzzle ({4,3}). And I found that to prevent the

> > small pieces in {4,3}, one has to make some circles into ellipses. And the

> > result is not that neat.

> >

> > Another solution to make a nice {4,3} of this kind is to change the size

> > of the face circles so that they are tangent to the edges. The puzzle would

> > be like this one (Gelatinbrain 3.5.2):

> >

> I made the {4,3} FEV puzzle you suggest, but it does have tiny pieces in

> MagicTile (due to interaction between edge and vertex circles). I haven’t

> added to the program yet, because I’d like your opinion between two

> options, one leaving the tiny pieces

> in<http://groups.yahoo.com/group/4D_Cubing/photos/album/1694853720/pic/1173747084/view?picmode=original&mode=tn&order=ordinal&start=1&dir=asc>,

> and one where the slice thickness is increased enough to avoid

> them<http://groups.yahoo.com/group/4D_Cubing/photos/album/1694853720/pic/115232229/view?picmode=original&mode=tn&order=ordinal&start=1&dir=asc>.

> Or maybe something else would be better. Let me know what you think.

>

> Roice

>