# Message #2591

From: schuma <mananself@gmail.com>

Subject: Re: RefleCube: a reflection on the Rubik’s Cube

Date: Wed, 02 Jan 2013 03:47:15 -0000

This is great. I also tried to do that on a physical 4x4x4.

———

I also analyzed what would happen on a reflect-megaminx:

First, because the axis of reflection passes a vertex and an edge, there’s no such thing like mirror+ or mirror X as on 3x3x3. Also, two reflections on the same face are equal to a twist. So the reflect-megaminx must be like mirror & twist.

A mirror move swaps two pairs of edges, applies no change to the fifth; swaps two pairs of corners and changes all five corners into the mirrored state.

The permutation of edges is always even, just like on a regular megaminx. The permutation of the stickers of edges is also even, which means flipping a single edge is impossible, just like on a regular megaminx.

The permutation of corners is even, just like on a regular megaminx. But orientation is special: you can MIRROR a single corner and have everything else solved. This is stronger than having a single corner ROTATED on a mirror & twist 3x3x3, because two mirror operation = one rotation but not the other way. The way to mirror a single corner is to mirror a pentagonal face, and then use an even number of moves to solve four corners and four edges, leaving one mirrored corner unsolved. And this is the only special thing about the reflect-megaminx.

Since twisting is allowed, the solution is mostly like a regular megaminx, until the end when you have to deal with some parity situations.

This puzzle can be simulated in MC4D by choosing

puzzle -> {5,3}x{} Dodecahedral Prism -> 3

There are two dodecahedra and 12 prisms. If you click on the prisms to scramble and solve the puzzle and ignore the dodecahedra, you are solving the reflect-megaminx.

————–

What about reflect-pyraminx? Every move swaps a pair of edges and a pair of corners, leaving three corners mirrored. Once the edges are solved or the corners are solved, the parities of everything are even like a normal pyraminx. So I think it’s very similar to pyraminx in terms of solving.

I’d say reflect-megaminx is more interesting than reflect-pyraminx.

Nan

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

>

> cool, I made checkerboards on both the 2^3 and 4^3 "Mirror & Twist" cubes!

> I remember probably 15 years ago setting out to try that on a physical

> 4^3, and giving up an hour or so later, mostly convinced it was impossible.

> And of course, what I was trying is impossible. But not here :)

>

> Happy New Year all,

> Roice

>

>

> On Sun, Dec 30, 2012 at 6:01 PM, schuma <mananself@…> 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

> >

> >

>