# Nautilus: A versatile 3x3 method



## Athefre (Mar 23, 2021)

*Nautilus Website*

Introducing a different kind of 3x3 method. The main first two steps are:

1. Solve a 1x2x3 on the left
2. Solve the dbr 2x2x2

Then the method has a few main variants afterward. Below are the main variants and additional variants are described on the website.

*L5E Variant:*

3. Solve the dFR pair (DFR corner and FR edge). The 2x2x2 + this pair can be solved in any other blockbuilding order. It is more efficient to solve these blocks in the best way for the situation.
4. CLL
5. L5E

*LL Variant:*

3. Solve the dFr square (DF edge, FR edge, and DFR corner). There are algorithms to orient all edges during Step 2 to make this square easily solvable using algorithms and to also always have ZBLL.
4. LL

*EOFE Variant:*

3. Orient all edges and solve the DF and FR edges in one algorithm.
4. Using option select orient the corners to lead to TTLL+, TTLL-, or PLL.
5. Finish with the TTLL+, TTLL-, or PLL algorithm.
Note: There are other sub-variants for EOFE such as reducing to L3C in step 4.

The primary shape of the Nautilus method is the left 1x2x3 and and the dbr 2x2x2. This is called the shell. This creates F2L minus a square. The shell can be solved using any other way. 1x2x3 then 2x2x2 is just the recommended strategy. The empty square can also be in any other position within F2L. For the variants, they range from easy to advanced. So anyone is able to get started without having to learn many algorithms. For those wanting to use a very advanced method, there are also variants for that. The variants for the method are designed to be a natural fit for the main shape formed by the 1x2x3 + 2x2x2.

Pros:

Great look-ahead for the rest of the solve after the 2x2x2 is built.
Most of the solve involves the use of only the dominant hand.
Good for both two handed and one handed solving.
Rotationless.
Low move-count.
Cons:

A lot of variants. Which can be seen as good or bad.
It isn't always best to use r, R, U, M. Some algorithms will instead need to be R, U, F.



Spoiler: Where to start



For the L5E variant, at the bottom of the Steps page on the site there is a Simplified and Intermediate section. This section provides an easy way for users to start and a set of steps for progression towards advanced L5E. The simplified option contains very few algorithms to memorize. The intermediate option is a very fast option that averages 48-50 moves and contains full CLL and L5EP.





Spoiler: History



I'm actually re-introducing this method, with a new name. This method is both new and old. I originally developed and proposed this almost 15 years ago in Summer-Fall of 2006 but have recently re-developed with a few new variants. It started with the MI1 method that can be seen in my signature. That method has a similar shape, except the DR edge isn't solved as part of the primary shape. I didn't like the ergonomics of the method occasionally requiring S moves and it also wasn't very suitable for good variants. So I decided to solve the DR edge as part of the first step. It then became a method of its own with a series of variants. Back then I had the L5E, LL, ZBLL, and LSLL variants. Additional, more unique variants were added starting late last year and can be seen on the website.

Since 2006, there have been a few methods proposed that are similar. Most notably the very cool M-CELL method which solves a 1x2x3, 2x2x2, the FR edge, then finishes with L5C and L5E. There is also Speed Heise-2 which solves a 1x2x3, 2x2x2, EO+DF edge, then the Speed Heise LSLL method. That is very similar to the LSLL variant of Nautilus. I'm sure there are others that have been mentioned in the New Method topic over the years. There are also other methods now that end with L5EP (which originated in MI1 in 2006). However, there is so much more potential in leaving the dFr square free. It provides a lot of freedom to work with the M and R layers.

An interesting thing to think about is that there are methods which solve the left side 1x2x3 then solve either the DF+DB edges or the right side 1x2x3 with EO mixed in at some point (more about that here). But with Nautilus, it is kind of 3D with blockbuilding being performed simultaneously on the M and R layers and EO at any point.



Check out the website and let me know if you have questions, suggestions, or variant ideas. Several algorithm sets have been generated so far. But there is still work to be done for the advanced variants and for discovering more about the method.

Join the Discord server:








Join the Nautilus Method Discord Server!


Check out the Nautilus Method community on Discord - hang out with 99 other members and enjoy free voice and text chat.




discord.gg


----------



## DNF_Cuber (Mar 23, 2021)

Is it named after the animal, or captain nemo's ship, or something else?


----------



## Athefre (Mar 23, 2021)

DNF_Cuber said:


> Is it named after the animal, or captain nemo's ship, or something else?



The animal. Because the blockbuilding order kind of looks like a spiral - the 1x2x3 going from the front to the back then to the 2x2x2 at dbr, then to the empty square at dFr.


----------



## PiKeeper (Mar 23, 2021)

Could you provide some example solves?


----------



## Athefre (Mar 23, 2021)

Mathsoccer said:


> Could you provide some example solves?



Sure, I can add examples. Though on the site there are some examples for the first part of the method. That is the most important thing to be highlighted in an example. For other steps, the example would only be representative of whatever algorithm case happens to occur in that scramble. But I can just add the continuation to those and note what variant is being used.


----------



## PiKeeper (Mar 23, 2021)

Thanks! Unless I'm mistaken, you only need to know of the variations to use the method, right? If so, it might be good if you showed the algorithm count and average moves for each variation so people can choose which path to start learning with. I'm not sure yet if I'll start learning this method, but it sounds interesting!


----------



## BenChristman1 (Mar 23, 2021)

So I’ve been messing around with this a tiny bit. From the 12 solves that I’ve done, I have a 44 average of 12. (I average about 16.5 with CFOP.) I also got a 19 single that was basically Petrus, so I’m not going to count that. I’ve been doing FB > 2x2x2 > DB edge > RB square > EO > last slot > 2-look CLL > L5EP. This definitely isn’t the best way to do it, but with the algs that I know now, it’s not terrible. I think that this method has a lot of potential, and I definitely think that globally sub-30 is possible with just a few days/weeks of practice.


----------



## Athefre (Mar 23, 2021)

Mathsoccer said:


> Thanks! Unless I'm mistaken, you only need to know of the variations to use the method, right? If so, it might be good if you showed the algorithm count and average moves for each variation so people can choose which path to start learning with. I'm not sure yet if I'll start learning this method, but it sounds interesting!



The number of algorithms for the variants that have been generated are mentioned in that variant's section and also for a couple of others. I guess I could specifically highlight that somewhere if that is what many desire. I am purposefully not providing the average move-count. This is due to recent methods using HARCS program numbers as representative of what humans can do. This has misled some members of the community and slightly altered expectations. Additionally, even if I did try to provide an exact number, it is actually impossible for that number to be perfect. I will say that the average movecount of most variants of this method will be around the same as Roux. More advanced variants will average 3-4 moves fewer.


----------



## trangium (Mar 25, 2021)

Athefre said:


> The number of algorithms for the variants that have been generated are mentioned in that variant's section and also for a couple of others. I guess I could specifically highlight that somewhere if that is what many desire. I am purposefully not providing the average move-count. This is due to recent methods using HARCS program numbers as representative of what humans can do. This has misled some members of the community and slightly altered expectations. Additionally, even if I did try to provide an exact number, it is actually impossible for that number to be perfect. I will say that the average movecount of most variants of this method will be around the same as Roux. More advanced variants will average 3-4 moves fewer.


You could, however, say how many moves each of the algorithm steps takes on average without any risk of being misleading. This way people could compare each of the Nautilus variants against each other.


----------



## Athefre (Mar 25, 2021)

trangium said:


> You could, however, say how many moves each of the algorithm steps takes on average without any risk of being misleading. This way people could compare each of the Nautilus variants against each other.



Yeah, I can do that. I actually recently calculated the average number of moves for some of the sets. So I'll just add them to the documents.


----------



## Athefre (Mar 25, 2021)

A Discord server has been created for the method. Join below:









Join the Nautilus Method Discord Server!


Check out the Nautilus Method community on Discord - hang out with 99 other members and enjoy free voice and text chat.




discord.gg


----------



## abunickabhi (Mar 26, 2021)

Interesting method. I just joined the server. Can't wait to follow the progress and optimization on all sub-steps.


----------



## PetraPine (Mar 28, 2021)

Mathsoccer said:


> Could you provide some example solves?



here's an example of doing block as 223+1 which is my favorite way to create it:








alg.cubing.net






alg.cubing.net




((also btw))- im now sub 15 with both the FB,222 and 223+1 "variants"


----------



## PetraPine (Mar 28, 2021)

Mathsoccer said:


> Thanks! Unless I'm mistaken, you only need to know of the variations to use the method, right? If so, it might be good if you showed the algorithm count and average moves for each variation so people can choose which path to start learning with. I'm not sure yet if I'll start learning this method, but it sounds interesting!


I'd recommend just starting out with the EO,OcLL PLL or OLL PLL since they will be what you are probably most familiar with, and EO is only 11 algs!


----------



## Athefre (Mar 29, 2021)

A more detailed explanation of the Nautilus name. The blockbuilding looks like a 3D version of the Fibonacci golden rectangle. This golden rectangle is often used to describe things in nature. It is most often associated with the Nautilus where the golden rectangle is layered over a Nautilus shell to show how the spiral of the shell matches the pattern. On a 3x3, when using the Nautilus method, the same pattern is created. Below is an image of the bottom of the cube. In the first step you build a 1x2x3, then after that a 2x2x2, then there are the remaining pieces. Starting with the empty pieces and going clockwise, it creates the pattern 1, 1, 2, 3. The 1x2x3 would extend to 3x3x3 on the left, but is restricted because it is a 3x3x3 cube.



I think we could have methods for other puzzles based on the Nautilus 3x3 method. The shape and concept of Nautilus should work well and provide some of the same freedom, ergonomics, and look-ahead. Big cubes, cuboids, minxes (though strange ergonomics in this case), and so on. I have a big cube version of Nautilus but haven't really posted yet.


----------



## PetraPine (Mar 29, 2021)

Athefre said:


> A more detailed explanation of the Nautilus name. The blockbuilding looks like a 3D version of the Fibonacci golden rectangle. This golden rectangle is often used to describe things in nature. It is most often associated with the Nautilus where the golden rectangle is layered over a Nautilus shell to show how the spiral of the shell matches the pattern. On a 3x3, when using the Nautilus method, the same pattern is created. Below is an image of the bottom of the cube. In the first step you build a 1x2x3, then after that a 2x2x2, then there are the remaining pieces. Starting with the empty pieces and going clockwise, it creates the pattern 1, 1, 2, 3. The 1x2x3 would extend to 3x3x3 on the left, but is restricted because it is a 3x3x3 cube.
> 
> View attachment 15249
> 
> I think we could have methods for other puzzles based on the Nautilus 3x3 method. The shape and concept of Nautilus should work well and provide some of the same freedom, ergonomics, and look-ahead. Big cubes, cuboids, minxes (though strange ergonomics in this case), and so on. I have a big cube version of Nautilus but haven't really posted yet.


I could ~try~ to make a nautilus method for megaminx, will update you if I find how to lol


----------



## Athefre (Mar 29, 2021)

What I was thinking is that you have those five pieces on the bottom right of a front layer. That would provide the same kind of movement as in Nautilus. It would also mean several variants could be used to finish. However, the ergonomics of moving the puzzle in that way aren't perfect.


----------



## PetraPine (Mar 29, 2021)

Athefre said:


> What I was thinking is that you have those five pieces on the bottom right of a front layer. That would provide the same kind of movement as in Nautilus. It would also mean several variants could be used to finish. However, the ergonomics of moving the puzzle in that way aren't perfect.


another variant you could make is kinda the way petrus is done on mega, were you get to last side and do EO (y') RB
you could simularly get to last side+one pair, EO, rfs , LL


----------



## Athefre (Mar 29, 2021)

ObscureCuber said:


> another variant you could make is kinda the way petrus is done on mega, were you get to last side and do EO (y') RB
> you could simularly get to last side+one pair, EO, rfs , LL



Let me know what you figure out. It would be nice to have something good for Megaminx that isn't LS+LL.


----------



## PetraPine (Mar 29, 2021)

Athefre said:


> Let me know what you figure out. It would be nice to have something good for Megaminx that isn't LS+LL.


the really sucks things about mega is that anything that doesn't go to LS>LL is really bad because of how the puzzle functions, I was trying it out, and while you can solve something like an extention of block, EO, its not worth doing because of how mega works.


----------



## Athefre (Apr 6, 2021)

L5E has been completed for Nautilus. This should make for one of the fastest variants.

*Nautilus L5E*


----------



## Cubing Forever (Apr 6, 2021)

Athefre said:


> L5E has been completed for Nautilus. This should make for one of the fastest variants.
> 
> *Nautilus L5E*


Those algs seem pretty good at first glance. I'll probably time test some of those if I get the time.


----------



## Luke Solves Cubes (Apr 8, 2021)

The method seems like every method that went up in popularity. Mark my words: "Someday there will be many people solving with Nautilus."


----------



## Rouxster (Jun 15, 2021)

Here are cll algs for the cx variant. These algs preserve EO and ignore the FR and FD edge.CXCOLL


----------



## Athefre (Jun 15, 2021)

Rouxster said:


> Here are cll algs for the cx variant. These algs preserve EO and ignore the FR and FD edge.CXCOLL



Nice! I'll add this link to the site and credit you. Thank you for putting this together. I've been busy with other projects so this is very helpful!


----------



## Athefre (Jul 7, 2021)

There have been some updates to the method. L5E is now the primary variant. The site has been updated accordingly. There is now a new Steps tab that goes over the steps of the L5E variant. The L5E variant has also been slightly modified to have the goal of blockbuilding the dbr 2x2x2 and dFR pair as one step. dbr 2x2x2 then dFR pair is efficient, but it is also sometimes best to solve the blocks in a different order. The L5E page also contains a simplified and intermediate option so that users can have a low alg count option and a way to progress towards advanced L5E. The rest of the Nautilus variants are all contained in the Other Variants tab.


----------



## PetraPine (Jul 8, 2021)

Athefre said:


> There have been some updates to the method. L5E is now the primary variant. The site has been updated accordingly. There is now a new Steps tab that goes over the steps of the L5E variant. The L5E variant has also been slightly modified to have the goal of blockbuilding the dbr 2x2x2 and dFR pair as one step. dbr 2x2x2 then dFR pair is efficient, but it is also sometimes best to solve the blocks in a different order. The L5E page also contains a simplified and intermediate option so that users can have a low alg count option and a way to progress towards advanced L5E. The rest of the Nautilus variants are all contained in the Other Variants tab.


I do wish one of the other variants came out on top
(like eo>square>LL)
the L5E variant (not accounting for the new algs) is quite the non-unique method, just a restrictive way of doing russo which honestly is quite a meh method.
I don't see why you like L5E so much?
It completely ruins what I found interesting in the first place (last square and eo)
just got a decent single on cam, didn't want to put it in another message:


----------



## Athefre (Jul 9, 2021)

ObscureCuber said:


> I do wish one of the other variants came out on top
> (like eo>square>LL)
> the L5E variant (not accounting for the new algs) is quite the non-unique method, just a restrictive way of doing russo which honestly is quite a meh method.
> I don't see why you like L5E so much?
> ...



I'm not throwing away the LL variant. It's still there at the top. And it certainly is a unique way to get to ZBLL. We can have more than one main variant. So users can still choose based on their preference. Everyone can debate which variant they think is best.

I chose to present L5E as the main variant on the site because the move-count is the same as or slightly lower than the ZBLL variant and it has the most potential for move-count improvement through the use of pseudo techniques. The L5E variant also has the most unique ending with L5E. Many methods end in ZBLL.

As for Russo and HK, Nautilus came first. And those two methods are pretty much saying "build this block however you want", which is strange.


----------



## StrategySam (Jul 12, 2021)

Isn't Nautilus a league of legends champ?


----------



## Athefre (Jul 12, 2021)

Maybe. It's also the name of a beautiful watch and there's a twisty puzzle by the name.


----------



## Cubing Forever (Jul 12, 2021)

Athefre said:


> Maybe. It's also the name of an beautiful watch and there's a twisty puzzle by the name.


Also don't forget Captain Nemo's submarine from 20,000 Leagues Under The Sea.


----------



## Athefre (Aug 14, 2021)

Development updates:

*New Variant:*

There has been a cool new variant proposed by trangium called EOFE. In this variant, after the shell all edges are oriented while solving the DF + FR edges. Then option select is used to orient the corners to where the final step is TTLL+, TTLL-, or PLL. Regular TTLL has worse algs than TTLL+, TTLL-, and PLL, so that set is avoided within the option select. We are also working on additional sub-variants for EOFE such as reducing to L3C.

*EOFE:*
1. 1x2x3 at dL
2. 2x2x2 at dbr
3. Orient all edges while solving the DF and FR edges
4. Using option select orient all corners to a TTLL+, TTLL-, or PLL case
5. Finish with the TTLL+, TTLL-, or PLL algorithm.

*CP Nautilus:*

CP first methods have gained some popularity recently. Each of them get to the CPEO2x2x3 state. I suggested that Nautilus could be a good alternative. For a more traditional CP first method, the steps would be:

1. CPFB
2. 2x2x2 at dbr
3. EO + DF edge
4. LSLL

This variant avoids having to recognize edge orientation of so many edges compared to previous CP methods. I also had the realization that CP can provide more benefits than just reducing to 2GLL. CP can greatly reduce the number of cases for other types of steps. So when CP Nautilus is used, each of the variants see a huge reduction in the number of algorithms required to learn and now some steps can even be combined. For example, trangium proposed setting up the FR edge to DF or FR then solve all corners + the FR edge then end with L5E. This would combine the dFR pair and CLL step of the L5E variant. Other variants receive the same kind of benefits and likely new CP-based variants can be discovered.

*Blockbuilding Examples:*

The website has been updated to include more blockbuilding strategies and examples. It covers the 2x2x2 and the 2x2x2 + dFR shape and the various ways in which they can be built. One goal is to create a blockbuilding sheet that provides solutions to many cases for each of the blockbuilding strategies.


----------



## Athefre (Aug 24, 2021)

Website updated. A tab for the LL variant and a tab for the EOFE variant has been added. The purpose is to make the identity of the method more clear. To make the other variants stand out more. L5E is a great variant, but isn't the only great one.

*L5E Variant:* Low move-count, works perfectly with pseudo.
*LL Variant:* Low move-count method for reaching ZBLL (or just LL), very unique step of solving the full empty square.
*EOFE Variant:* Allows for many sub-variants, incorporates option select with great recognition.


----------



## LBr (Sep 19, 2021)

which variant do you think is the best for oh, and what would your top tips be if, say, I switched to it for oh?


----------



## OreKehStrah (Sep 19, 2021)

LBr said:


> which variant do you think is the best for oh, and what would your top tips be if, say, I switched to it for oh?


I would guess the l5e approach would be best for OH if you don't wanna have to learn a lot of ZBLL. Most of the l5e algs look pretty good for OH if you use table abuse for MU


----------



## voidrx (Sep 19, 2021)

OreKehStrah said:


> I would guess the l5e approach would be best for OH if you don't wanna have to learn a lot of ZBLL. Most of the l5e algs look pretty good for OH if you use table abuse for MU


Actually the LSLL variant, more specifically, the EODF->CLPS->2GLL is considered OO with L5E very slightly behind for OH


----------



## Chemnitz (Sep 20, 2021)

LBr said:


> which variant do you think is the best for oh, and what would your top tips be if, say, I switched to it for oh?


Void has requested that I address some curiosity about OH Nautilus. I am the fastest person, to our knowledge, who seriously uses OH Nautilus. Here's my two cents:

On Nautilus:
If you want to switch to Nautilus completely, learn L5E. The alg count for 2 look L5E is low and the Nautilus community has developed several intermediate methods for learning full L5E. L5E is also near the top for OH, so having this one variant is sufficient to be quite good at 2H and OH.

On OH Nautilus:
The OH situation is a bit odd, as we have several variants that could be quite good and a few that are completely unviable (Looking at you, CX). Based on my experience with OH and my understanding/testing of each variant, albeit in their most intuitive forms, this is the conclusion I have come to: If you want just an OH method and plan to keep a different method for 2H, L5E is not the best. Here are my rankings of the most viable OH variants for Nautilus:

Clear Winner:

CPLS aka Corner Permutation Last Slot (Specific path for Last Slot Last Layer variant):
Shell
Edge Orientation + DF edge (Mostly intuitive, I would argue there are less than 10 cases worth learning algs for)
CPLS (Identical to ZZ's CPLS, solve the FR pair while permuting corners. RUL and RUD with a few decent RUF algs. Around 100 cases)
2GLL (84 ZBLLs, RU gen)

Runner Ups:

L5E aka Last Five Edges:
Shell
FR Pair
NCLL (42 algs)
L5E (245 algs)

EOFE aka Edge Orientation Front Edges:
Shell
EO + F2L edges
Finish (Several paths, CPLS -> 2GLL looking best for OH)

Starters (not the best, used while learning their advanced forms):

L5E2 aka Two Look Last Five Edges:
Shell
FR Pair
NCLL (Still 42 algs)
L5EO (Intuitive)
L5EP(16 algs)

CPInsert aka Corner Permutation during Insert (LSLL path):
Shell
EO+DF (Less than 10 algs)
Setup to 3 move insert CPLS
CPLS (few LS cases)
2GLL (84 cases)


----------



## DuckubingCuber347 (Oct 4, 2021)

*On average *which is more efficient for 2-look L5E, inserting DF and then ELL or EO followed by L5EP? I understand that there are plenty of cases where one would be more efficient I just want to know which is better on average.


----------



## voidrx (Oct 4, 2021)

TheCubingCuber347 said:


> *On average *which is more efficient for 2-look L5E, inserting DF and then ELL or EO followed by L5EP? I understand that there are plenty of cases where one would be more efficient I just want to know which is better on average.


EO+L5EP.


----------



## DuckubingCuber347 (Oct 4, 2021)

voidrx said:


> EO+L5EP.


And how is that?


----------



## voidrx (Oct 4, 2021)

TheCubingCuber347 said:


> And how is that?


@trangium 's ELLs, which are the best out there that I know of average 10.27 moves. inserting the DF edge is around 3 moves + AUF, so around 3.75. 3.75+10.27= 14.02 moves.
Now. EO averages around 5 moves. L5EP averages 7.38 moves according to the Nautilus L5E algsheet. 7.38+5=12.38 however we need to include AUF so add 1.5 moves (two AUFs), that makes 13.88. 
EO+L5EP is more efficient than DFM+ELL.


----------



## DuckubingCuber347 (Oct 5, 2021)

voidrx said:


> Now. EO averages around 5 moves. L5EP averages 7.38 moves according to the Nautilus L5E algsheet. 7.38+5=12.38 however we need to include AUF so add 1.5 moves (two AUFs), that makes 13.88.


L5EO has 5 cases with 7, 7, 7, 7, 3 moves (excluding AUF). Wouldn't that be 6.06? Or are the EO algs on the Nautilus website not good movecount wise?
6.06+7.3 = 13.44 + AUF[=.75 x 2] = 14.98
 (technically 13.45 since 6.06=6.0625)

Am I just being stupid?

Edit: Where do I find trangiums ELL's?
Edit Edit: nvm they're on his Github.


----------



## voidrx (Oct 5, 2021)

TheCubingCuber347 said:


> L5EO has 5 cases with 7, 7, 7, 7, 3 moves (excluding AUF). Wouldn't that be 6.06? Or are the EO algs on the Nautilus website not good movecount wise?
> 6.06+7.3 = 13.44 + AUF[=.75 x 2] = 14.98
> (technically 13.45 since 6.06=6.0625)
> 
> ...


Ok. I miscounted. So DFM+ELL is slightly more efficient. HOWEVER. That does not mean that DFM+ELL is as fast as EO+L5EP. EO has amazing recog. DFM has great recog. Now ELL recog is kind of eh. L5EP recog is very good. EO+L5EP is faster, as it sacrifices one move for way better recog.


----------



## tsmosher (Oct 7, 2021)

TheCubingCuber347 said:


> And how is that?



By my estimation, rounding up to imprecisely account for AUF:

L5EOP: 7.5 moves (20 cases)
EPLL: 7 moves (4 cases)
= 14.5 moves (24 cases)

L5EO: 6.5 moves (5 cases)
L5EP: 8 moves (16 cases)
= 14.5 moves (21 cases)

place DF: 3.5 to 4 moves (intuitive)
ELL: 11 moves (29 cases)
= 14.5 to 15 moves (29 cases)

The ELL approach might be comparable if you omit the case where the DFM edge is flipped in DFM.

They definitely all seem to be pretty close.


----------

