Message #2582

From: Melinda Green <melinda@superliminal.com>
Subject: Re: [MC4D] Re: RefleCube: a reflection on the Rubik’s Cube
Date: Sun, 30 Dec 2012 17:41:11 -0800

Awesome, Nan!

Would someone please calculate the number of unique positions in the 2^3
Mirror+, MirrorX or Half turn puzzles? If their state graphs are small
enough we might learn something about the common features of puzzle
state graphs. By "unique" I mean that it should not be possible to
rotate the whole puzzle from one state into another, nor should it be
possible to recolor one state to produce another one.

Thanks for the new puzzles Nan!
-Melinda

On 12/30/2012 4:01 PM, schuma wrote:
> Hi RefleCube solvers. Thank you all for your support.
>
> Since you guys find these puzzles interesting and have solved them quickly, I just added several sizes: 2x2, 4x4 and 5x5. For each size all the mirroring styles are supported. Use shift+click and alt+click to turn the deeper layers.
>
> Imagine what kind of weird parities you’ll see on the 4x4. Have fun!
>
> Nan
>
> — In 4D_Cubing@yahoogroups.com, "Andrey" <andreyastrelin@…> wrote:
>> Nice puzzle!
>> Mirror+ and mirrorX solved, no special operations required :) Now trying mixed puzzle…
>>
>> Andrey
>>
>> — In 4D_Cubing@yahoogroups.com, "schuma" <mananself@> wrote:
>>> Hi guys,
>>>
>>> Recently I made a puzzle simulator called RefleCube:
>>>
>>> http://nanma80.github.com/
>>>
>>> The idea is, instead of twisting a layer by 90 degrees like on the Rubik’s Cube, we can mirror a layer. For example, the top layer (U) can be mirrored with respect to the plane bisecting the cube into left and right halves. The result of the reflection is swapping UFR with UFL, UBR with UBL, UR with UL.
>>>
>>> We can also think of reflecting a layer with respect to a diagonal plane so that UFR<->UBL, UF<->UL, UR<->UB.
>>>
>>> I call the first transform "mirror +", and the second transform "mirror X".
>>>
>>> You can choose to play a puzzle with only one type of mirroring moves, or both of them (which implies the Rubik’s Cube’s twisting moves).
>>>
>>> I also included the common Rubik’s cube and a half-turn cube (only allows 180 degree turns) because they are related.
>>>
>>> This puzzle is inspired by Magic Cube 2D (http://www.superliminal.com/cube/mc2d.html) and the discussion about it. I also emulated this puzzle using MC4D and MPUlt before implementing it. You know, we can use 4D rotation to emulate 3D reflection.
>>>
>>> I’m not going to tell you what can happen or cannot happen on RefleCube. Find out by yourself!
>>>
>>> Nan
>>>
>
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