# Message #1903

From: schuma <mananself@gmail.com>

Subject: Re: {7,3} vertex and edge turning puzzles

Date: Tue, 08 Nov 2011 06:33:42 -0000

Hi Roice,

Thank you for making these two puzzles. They are pretty neat indeed. I just solved both of them and I enjoy solving them. The FT {7,3} is to the Rubik’s cube as the VT {7,3} is to the Dino Cube (with stationary corners), as the ET {7,3} is to the helicopter cube (a better analog is TomZ’s Curvy Copter).

The feeling of solving ET and VT was just like solving the "classic" face turning {7,3}. In principle they are very close to classic puzzles. So, pretty easy, a little bit tedious because of their size, but the geometry keeps the procedure interesting.

Comparing the depth of cuts in ET{7,3} and ET{3,7}, I wonder what’s the unit of depth. If the length of a side is the unit, then they have similar depth. But I think a better comparison is to count the number of circles that each circle intersects with. So I would say ET {7,3}’s cuts are much shallower and therefore it has much less pieces. The same for the VT puzzles.

The ET{7,3} puzzle has stationary centers, rotation-only 2C edges, 3C corners and 1C triangles. The 1C triangles are in 21 orbits just like the corresponding pieces in ET{3,7}. But here we have stationary centers as references, thus we don’t need to deduce the global orientation. Also, after solving the 2C edges, the eight 1C triangles in each orbit must be in even permutation, making the situation easier than the regular helicopter cube.

They are overall easy puzzles and I love them. I do solve complicated puzzles but I love the simple ones. Thanks.

Nan

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

>

> Hi Nan,

>

> If you download the

> latest<http://www.gravitation3d.com/magictile/downloads/MagicTile_v2_Preview.zip>,

> you’ll now see vertex and edge turning versions of the {7,3}. They are quite

> beautiful<http://groups.yahoo.com/group/4D_Cubing/photos/album/1694853720/pic/104211987/view?picmode=&mode=tn&order=ordinal&start=1&count=20&dir=asc>when

> scrambled.

>

> I picked depths that felt like a nice balance, but they can be changed. I

> made the ET slightly deeper than I did for the {3,7}. It seemed better to

> do so in this case. I wonder if the {7,3} ET will also have some

> intriguing piece orbits, like you observed on the {3,7}.

>

> If you are interested in a more detailed write up on how to edit slicing

> circles and their depths, let me know. It requires hand editing the puzzle

> config files, but the format is pretty simple. It is based on discussion

> we had in the past - you can enter depths as multiples of

> incircles/circumcircles/edge lengths, or you can enter them as an absolute

> distance.

>

> In any case, I am happy to configure files for any puzzles you describe,

> assuming MagicTile can support them.

>

> Roice

>

> P.S. This version also removes the duplicate color you found in the

> default settings. Thanks for noticing that :)

>

>

>

> On Mon, Nov 7, 2011 at 2:56 AM, Nan Ma <mananself@…> wrote:

>

> >

> >

> > Hi Roice,

> >

> > About the Klein quartic, I’m curious if the vertex turning and edge

> > turning {7,3} can be made. They have less colors than the {3,7}

> > counterparts. So it should be easier to find pieces on them. Thanks.

> >

> > Nan

> >

>