Curvy Copter algs

[mrCage]

Hi!

I challenge anyone to come up with a shortest possible way (please provide sequence or description) to flip all the 12 middle edges of the curvy copter. So far i am down to 72 turns but still improving. It is quite fun but aggrevating also ...

Per

[mrCage]

One can use the following 26 turns to make up a complete 12-flip solution in 58 turns. I show part 1 only. Part 2 is same on the other half.
It is done like so: part1 + setup + part2 + unsetup.

Part1:

/*000000*/BD,
/*000001*/RB,
/*000002*/DR,
/*000003*/BD,
/*000004*/DR,
/*000005*/BD,
/*000006*/DR,
/*000007*/BD,
/*000008*/RB,
/*000009*/BD,
/*000010*/DR,
/*000011*/RB,
/*000012*/DR,
/*000013*/FU,
/*000014*/RF,
/*000015*/UR,
/*000016*/FU,
/*000017*/UR,
/*000018*/FU,
/*000019*/UR,
/*000020*/FU,
/*000021*/RF,
/*000022*/FU,
/*000023*/UR,
/*000024*/RF,
/*000025*/UR,

Copy and paste into gelatinbrain applet to verify. It flips 6 edges and twists 2 corners. Yay!!

Per

PS! I really miss a "play" feature on gelatinbrain. Should be quite easy to implement i guess ...

[mrCage]

No, this is not another "fyou have been framed" post. This is serious! It has previously been proven that 2 adjacent edges cannot be flipped without jumbling. However 2 opposite edges (FR and BL) can be flipped, and i will constructively show how. For sure not the shortest way possible, but it does the trick.

First i will flip 6 edges with 2-part sequence:
DB DR UR UF FR [UR UF]3 FR UF UR FR DR DB (17 turns)
RF RD DL BL BD [DL BL]3 BD BL DL BD RD RF (17 turns)

Now we have a 6-flip!

Next we flip 4 of those edges:
[UR UF]3 UB UL BL FR DR DF [DB DL]3 DF DR FR BL UL UB (24 turns)

Altogether a dreadful 58 turns, same as i currently have for my 12-flip (also no jumbling).

Per

PS!

Copy and paste this ugly sequence into gelatin curvy copter applet to verify my sequence(s).

/*000000*/BD,
/*000001*/RD,
/*000002*/UR,
/*000003*/FU,
/*000004*/RF,
/*000005*/UR,
/*000006*/FU,
/*000007*/UR,
/*000008*/FU,
/*000009*/UR,
/*000010*/FU,
/*000011*/RF,
/*000012*/FU,
/*000013*/UR,
/*000014*/RF,
/*000015*/RD,
/*000016*/BD,
/*000017*/RF,
/*000018*/RD,
/*000019*/DL,
/*000020*/LB,
/*000021*/BD,
/*000022*/DL,
/*000023*/LB,
/*000024*/DL,
/*000025*/LB,
/*000026*/DL,
/*000027*/LB,
/*000028*/BD,
/*000029*/LB,
/*000030*/DL,
/*000031*/BD,
/*000032*/RD,
/*000033*/RF,
/*000034*/UR,
/*000035*/FU,
/*000036*/UR,
/*000037*/FU,
/*000038*/UR,
/*000039*/FU,
/*000040*/UB,
/*000041*/LU,
/*000042*/RF,
/*000043*/LB,
/*000044*/RD,
/*000045*/DF,
/*000046*/DL,
/*000047*/BD,
/*000048*/DL,
/*000049*/BD,
/*000050*/DL,
/*000051*/BD,
/*000052*/DF,
/*000053*/RD,
/*000054*/RF,
/*000055*/LB,
/*000056*/LU,
/*000057*/UB,
Per

It can be reduced by at least 12 turns when inserting the 4-flip into the 6-flip. Please feel free to work it out ...

[mrCage]

My lemma. This is the only 2-flip scenario possible on the curvy copter with no jumbling sequences!!

Per

[mrCage]

I'm gonna sketch a proof for my own lemma. Make complete map of the 4 center orbitals. The only place that 2 center orbitals "cross" over another edge (after first flip) is on the opposite side of the puzzle. This can be done like so (disregarding corners, that can trivially be restored):

/*000000*/UB,
/*000001*/UR,
/*000002*/LU,
/*000003*/RF,
/*000004*/FL,
/*000005*/BR,
/*000006*/LB,
/*000007*/RD,
/*000008*/DL,
/*000009*/DF,
/*000010*/DL,
/*000011*/RD,
/*000012*/LB,
/*000013*/BR,
/*000014*/FL,
/*000015*/RF,
/*000016*/LU,
/*000017*/UR,

Bolded part is setup turns! So: first swap around UB, setup, then swap around DF. Etc ....

Per

[mrCage]

I completed the above sequence with solving the 4 corners also. Slight optimisations gave me this:

/*000000*/UB,
/*000001*/RF,
/*000002*/FU,
/*000003*/RF,
/*000004*/UR,
/*000005*/RF,
/*000006*/FU,
/*000007*/RF,
/*000008*/LU,
/*000009*/RF,
/*000010*/FL,
/*000011*/BR,
/*000012*/LB,
/*000013*/RD,
/*000014*/DL,
/*000015*/DF,
/*000016*/DL,
/*000017*/RD,
/*000018*/LB,
/*000019*/BR,
/*000020*/FL,
/*000021*/RF,
/*000022*/LU,
/*000023*/FU,
/*000024*/UR,
/*000025*/UB,
/*000026*/UR,
/*000027*/FU,
/*000028*/UR,
/*000029*/UB,
/*000030*/UR,
/*000031*/FU,
/*000032*/UR,
/*000033*/FU,

34 non-jumbling turns for an edge 2-flip!!

Per

[mrCage]

Here i will post any (best cases only) edge flipping algorithms that i have found for the curvy copter. These are invisible on the normal helicopter cube!!

First one out of the sack is the 12-flip. This one has a long story behind it, but i will spare you the details and just post the sequence:

/*000000*/UB,
/*000001*/UR,
/*000002*/RF,
/*000003*/BR,
/*000004*/RD,
/*000005*/LU,
/*000006*/FL,
/*000007*/LB,
/*000008*/DL,
/*000009*/BD,
/*000010*/DF,
/*000011*/LU,
/*000012*/FL,
/*000013*/LU,
/*000014*/FL,
/*000015*/LU,
/*000016*/FL,
/*000017*/DL,
/*000018*/LB,
/*000019*/FL,
/*000020*/LU,
/*000021*/DL,
/*000022*/LB,
/*000023*/DL,
/*000024*/LB,
/*000025*/DL,
/*000026*/LB,
/*000027*/UR,
/*000028*/RF,
/*000029*/UR,
/*000030*/RF,
/*000031*/UR,
/*000032*/RF,
/*000033*/RD,
/*000034*/BR,
/*000035*/RF,
/*000036*/UR,
/*000037*/RD,
/*000038*/BR,
/*000039*/RD,
/*000040*/BR,
/*000041*/RD,
/*000042*/BR,
/*000043*/FU,



Per

PS! More flips will follow when i get the time, and please feel free to contribute.

[Godmil]

It seems like your pretty much on your own with the love for the Curvy Copter
I'm curious now though, think I'll buy one, which do you recommend?

[mrCage]

Right. I guess i'm a slow solver But if you should choose between a helicopter cube and a curvy copter one. Get the curvy, unless the extra edge solving annoys you. Cheaper and better turning quality

Per

[mrCage]

Ok, i will add more flip cases. Now a 2-flip from another thread.

/*000000*/UB,
/*000001*/RF,
/*000002*/FU,
/*000003*/RF,
/*000004*/UR,
/*000005*/RF,
/*000006*/FU,
/*000007*/RF,
/*000008*/LU,
/*000009*/RF,
/*000010*/FL,
/*000011*/BR,
/*000012*/LB,
/*000013*/RD,
/*000014*/DL,
/*000015*/DF,
/*000016*/DL,
/*000017*/RD,
/*000018*/LB,
/*000019*/BR,
/*000020*/FL,
/*000021*/RF,
/*000022*/LU,
/*000023*/FU,
/*000024*/UR,
/*000025*/UB,
/*000026*/UR,
/*000027*/FU,
/*000028*/UR,
/*000029*/UB,
/*000030*/UR,
/*000031*/FU,
/*000032*/UR,
/*000033*/FU,



Per