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 o=
n 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; swa=
ps two pairs of corners and changes all five corners into the mirrored stat=
e.
The permutation of edges is always even, just like on a regular megaminx. T=
he 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 or=
ientation is special: you can MIRROR a single corner and have everything el=
se solved. This is stronger than having a single corner ROTATED on a mirror=
& twist 3x3x3, because two mirror operation =3D one rotation but not the o=
ther 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 a=
bout 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=20
puzzle -> {5,3}x{} Dodecahedral Prism -> 3
There are two dodecahedra and 12 prisms. If you click on the prisms to scra=
mble and solve the puzzle and ignore the dodecahedra, you are solving the r=
eflect-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 pyram=
inx. 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
>
> 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 impossibl=
e.
> And of course, what I was trying is impossible. But not here :)
>=20
> Happy New Year all,
> Roice
>=20
>=20
> On Sun, Dec 30, 2012 at 6:01 PM, schuma
>=20
> > 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 al=
l
> > the mirroring styles are supported. Use shift+click and alt+click to tu=
rn
> > the deeper layers.
> >
> > Imagine what kind of weird parities you'll see on the 4x4. Have fun!
> >
> > Nan
> >
> >
>