{8,3} 10 colors puzzle is an another strange beast. It has four faces of or=
der 2 (i.e. each of them has only 2 neighbors), two faces of order 4 and 4 =
"irregular" faces. And if you start to solve it from order 2 faces (that is=
good idea because puzzle is the most dense there), you find yourself in si=
tuation where you have two disjoint unsolved "layers" - around order 4 face=
s - and have to sort pieces and exchange parity/orientation between them (l=
ike when you solve 3^3 starting with the middle layer).
And there is a chance to meet parity problem: some 2C pieces are identica=
l and if odd number of pairs are swapped, you'll need to solve it (by swapp=
ing some pair once more). And repeat sorting of order 4 layers again :)
Nice thing :)
Andrey
=20=20
------=_NextPart_000_0037_01CD9DAA.52819E80
Content-Type: text/plain;
charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable
A MT fan is born!
27 solutions (more than Melinda! ;-) )
I think you talk about the face turning puzzle.
----- Original Message -----=20
From: Andrey=20
To: 4D_Cubing@yahoogroups.com=20
Sent: Friday, September 28, 2012 11:02 AM
Subject: [MC4D] MT {8,3} 10 colors
=20=20=20=20
{8,3} 10 colors puzzle is an another strange beast. It has four faces of =
order 2 (i.e. each of them has only 2 neighbors), two faces of order 4 and =
4 "irregular" faces. And if you start to solve it from order 2 faces (that =
is good idea because puzzle is the most dense there), you find yourself in =
situation where you have two disjoint unsolved "layers" - around order 4 fa=
ces - and have to sort pieces and exchange parity/orientation between them =
(like when you solve 3^3 starting with the middle layer).
And there is a chance to meet parity problem: some 2C pieces are identica=
l and if odd number of pairs are swapped, you'll need to solve it (by swapp=
ing some pair once more). And repeat sorting of order 4 layers again :)
Nice thing :)
Andrey
=20=20
------=_NextPart_000_0037_01CD9DAA.52819E80
Content-Type: text/html;
charset="iso-8859-1"
Content-Transfer-Encoding: quoted-printable
{8,3} 10 colors puzzle is an another strange beast. It has four faces =
of=20
order 2 (i.e. each of them has only 2 neighbors), two faces of order 4 an=
d 4=20
"irregular" faces. And if you start to solve it from order 2 faces (that =
is=20
good idea because puzzle is the most dense there), you find yourself in=20
situation where you have two disjoint unsolved "layers" - around order 4 =
faces=20
- and have to sort pieces and exchange parity/orientation between them (l=
ike=20
when you solve 3^3 starting with the middle layer).
And there is a cha=
nce=20
to meet parity problem: some 2C pieces are identical and if odd number of=
=20
pairs are swapped, you'll need to solve it (by swapping some pair once mo=
re).=20
And repeat sorting of order 4 layers again :)
Nice thing=20
:)
Andrey
--------------090908060502090402000202
Content-Type: text/plain; charset=ISO-8859-1; format=flowed
Content-Transfer-Encoding: 7bit
Definitely interesting. 2 questions come to mind.
1. Can you construct a puzzle in which all the octagonal edges contain
digons, and
2. Can you flip some or all edges in order to create non-orientable
versions?
-Melinda
On 10/4/2012 8:15 PM, Roice Nelson wrote:
> Cool stuff! Taking a look, the underlying abstract shape has 10
> faces, 24 edges, and 16 vertices. So its Euler Characteristic is 2,
> and it has the topology of the sphere. This means the graph of it can
> be drawn on the plane:
>
> http://www.gravitation3d.com/magictile/pics/83/83-10_graph.png
>
> Here is the unrolled version for reference:
>
> http://www.gravitation3d.com/magictile/pics/83/83-10_unrolled.png
>
> The first pic nicely shows how by starting your solution with the
> digons (the "order 2" faces), it will be similar to solving a 3^3
> starting with the middle layer.
>
> The "irregular" octagonal faces are interesting. I initially thought
> these faces were hexagons in the abstract, until I realized they
> shared multiple disjoint edges with the same neighbor. I hadn't seen
> anything like that before.
>
> Cheers,
> Roice
>
>
> On Fri, Sep 28, 2012 at 4:02 AM, Andrey
>
> {8,3} 10 colors puzzle is an another strange beast. It has four
> faces of order 2 (i.e. each of them has only 2 neighbors), two
> faces of order 4 and 4 "irregular" faces. And if you start to
> solve it from order 2 faces (that is good idea because puzzle is
> the most dense there), you find yourself in situation where you
> have two disjoint unsolved "layers" - around order 4 faces - and
> have to sort pieces and exchange parity/orientation between them
> (like when you solve 3^3 starting with the middle layer).
> And there is a chance to meet parity problem: some 2C pieces are
> identical and if odd number of pairs are swapped, you'll need to
> solve it (by swapping some pair once more). And repeat sorting of
> order 4 layers again :)
> Nice thing :)
>
> Andrey
>
>
>
>
--------------090908060502090402000202
Content-Type: text/html; charset=ISO-8859-1
Content-Transfer-Encoding: 7bit
http-equiv="Content-Type">
Definitely interesting. 2 questions come to mind.
contain digons, and
non-orientable versions?
-Melinda
wrote:
type="cite">Cool stuff! Taking a look, the underlying abstract
shape has 10 faces, 24 edges, and 16 vertices. So its Euler
Characteristic is 2, and it has the topology of the sphere. This
means the graph of it can be drawn on the plane:
the digons (the "order 2" faces), it will be similar to solving
a 3^3 starting with the middle layer.
thought these faces were hexagons in the abstract, until I
realized they shared multiple disjoint edges with the same
neighbor. I hadn't seen anything like that before.
wrote:
{8,3} 10
colors puzzle is an another strange beast. It has four faces
of order 2 (i.e. each of them has only 2 neighbors), two faces
of order 4 and 4 "irregular" faces. And if you start to solve
it from order 2 faces (that is good idea because puzzle is the
most dense there), you find yourself in situation where you
have two disjoint unsolved "layers" - around order 4 faces -
and have to sort pieces and exchange parity/orientation
between them (like when you solve 3^3 starting with the middle
layer).
And there is a chance to meet parity problem: some 2C pieces
are identical and if odd number of pairs are swapped, you'll
need to solve it (by swapping some pair once more). And repeat
sorting of order 4 layers again :)
Nice thing :)
Andrey
--------------090908060502090402000202--