# Message #2231

From: Roice Nelson <roice3@gmail.com>

Subject: Re: [MC4D] "Three strange {8,4} colorings"

Date: Sat, 02 Jun 2012 09:58:53 -0500

Melinda asked if I could add FEV versions for the {8,4} puzzles, so they

are available now<http://www.gravitation3d.com/magictile/downloads/MagicTile_v2.zip>

.

For the other FEV puzzles we’ve discussed, I set the E and V cut diameters

to the tiling edge length, then made the F cuts tangent to the V cuts. On

the {8,4} tilings, you get some tiny pieces with this approach, so I made

the {8,4} FEV puzzles slightly different. The V cut is still equal to the

tile edge length and the F cut is still tangent to it (on this tiling, they

turn out to have the same radius), but I configured the E cut slightly

smaller. It is set to intersect where the F and V cuts are tangent. I

like the result<http://groups.yahoo.com/group/4D_Cubing/photos/album/1694853720/pic/1893562896/view?picmode=large>.

49 stickers per face.

Cheers,

Roice

On Fri, Jun 1, 2012 at 10:22 AM, Roice Nelson <roice3@gmail.com> wrote:

> I can’t help in the solution department, but here is some basic info about

> the topologies :)

>

> *{8,4} 5-Color*

> Faces 5

> Edges 8

> Vertices 4

> Euler Characteristic 1

>

> *{8,4} 9-Color*

> Faces 9

> Edges 16

> Vertices 8

> Euler Characteristic 1

>

> *{8,4} 10-Color*

> Faces 10

> Edges 16

> Vertices 8

> Euler Characteristic 2

>

> So the first two have the topology of the projective plane

> (non-orientable), and the last of the sphere.

>

> Anyone want to figure out counts and kinds (henagons, digons, etc.) of the

> particular faces? The 10C should have a nice, planar graph representation.

> Roice

>

>

> On Fri, Jun 1, 2012 at 5:23 AM, Melinda Green <melinda@superliminal.com>wrote:

>

>> That was about all that Roice said about these three puzzles and nobody

>> seems to have noticed them. That’s understandable because he was

>> dropping hundreds of new puzzles on us at the same time and the {8,4}s

>> were at the very end. Well I stumbled into them a couple of days ago and

>> can say "Mighty strange indeed!" As you know, I’ve been focusing on

>> edge-turning puzzles that I can solve intuitively and found the 5-color

>> and 10-color versions to be a lot of fun. They start out easy enough and

>> finish with enough of a brain stretch to be quite rewarding to solve. I

>> had tried and failed with with the 9-color version after a couple of

>> half-hearted attempts, but since I had solved the other two I figured it

>> was time to make a serious attempt to collect all three, and all I can

>> say is "OH………………………….., MY GOD!" Roice mentioned

>> that they have some interesting topological properties that would be fun

>> to study and I completely agree. The best single word I can find to

>> describe tthe 9-color version is "perverse". Rather than try to

>> describe what I found, I want to invite Ed and Nan and any other serious

>> puzzlers to give these a shot. Then please let us know what you think.

>> Do they yield easily to your standard methods? Do the face and vertex

>> turning version behave as oddly as the edge-turning? I definitely want

>> to learn more about these bad boys!

>>

>> -Melinda

>>

>