# Message #2158

From: Melinda Green <melinda@superliminal.com>

Subject: Re: [MC4D] Re: Edge turning {3,7} IRP solved

Date: Mon, 14 May 2012 00:55:32 -0700

I think you mean the {3,9}a 36-Color (there is no 24-color version), and

yes, that is the right answer. You are also right that each orbit only

intersects itself once, not three times. That happens in a figure-8

pattern. This gives it the strange property of allowing you to swap a

single edge in isolation. When I saw that state during my solve I

naturally thought that I had another duplicate color hiding somewhere

but searching for it turned up nothing. I then figured that I would

probably have to use the fact that its orbit self-intersects in order to

solve it and sure enough that worked.

This puzzle is an especially lovely and symmetric object and closely

related to the {3,7}. I think you can really see it as a kind of union

of two {3,7}’s. You can build a {3,7} by starting with an icosahedron

and attaching 4 octahedra to 4 of its faces along tetrahedral axes in a

pattern of carbon bonds in a diamond lattice. That uses up 4 of each

icosahedron’s 20 faces. Well you can make this {3,9} by adding yet

another 4 octrahedra in another diamond lattice. It is therefore much

denser and difficult to see well in MT 3D mode but rotating it around or

viewing in stereo will show you what I mean.

So here is a new challenge: Find the shortest way to flip a single edge

of this lovely IRP.

Enjoy!

-Melinda

On 5/13/2012 10:08 PM, schuma wrote:

> Hi Melinda,

>

> I can see {3,9}a 24-Color E0:1:0 is close, but not exact. There, an orbit can visit a triangle twice, from two directions, but not three times. I haven’t found a similar property on other {3,n} puzzles. But, for those puzzles where the faces are not equivalent, I cannot exclude them unless I have tried all the faces.

>

> Can you reveal the answer now?

>

> Nan

>

> — In 4D_Cubing@yahoogroups.com, Melinda Green<melinda@…> wrote:

>> There is also at least one puzzle in which paths loop around and crosses

>> itself kind of like the shape of the number 6. Because of that you can

>> move a petal from one corner of a triangle, sending it out around its

>> orbit only to come back in such a way that you can place it into a

>> different corner of the triangle that it came from. The orbit must loop

>> around three times like that like a Celtic triangle

>> <http://www.clker.com/cliparts/z/d/7/8/q/C/celtic-triangle-md.png>. I’ll

>> let you figure out which puzzle that is. :-)

>

>

>

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