EO Steps

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The term EO Step refers to the 3x3x3 first substeps which orient most of the edges while simultaneously solving other pieces. They are most commonly used in the ZZ method, although they can be applied to other methods as well.

The initial EO step from which the others were later derived is EOLine, invented by Zbigniew Zborowski.

The steps are ordered from easiest to hardest.


EO+X consists of firstly orienting all twelve edges and then solving other pieces separately. For example, EO+Line would be to solve EO and then the DF and DB edges, while the latter step is not influenced in any way during EO. Although very easy and often used by beginners, this approach makes the solve less efficient and require at least two looks.



EODB is used in the Portico method by Matt DiPalma and solves the DB edge after EO.


  • Allows for more efficient ZZ F2L by being able to use F2 and M' U2 M.
  • Very easy to plan which leads to easier inspection.


  • DF edge needs to be solved later.
  • F2 and M' U2 M in the middle of the solve often require regrips and might not save as much time.
  • Lookahead can be hindered by the unsolved DF edge.



pEOLine is used in ZZ-top and consists of solving the DF and DB edges like in EOLine. However, since only the F2L edges are oriented, this is called pEOLine (partial EOLine). Only orienting these edges leads to easier planning but a worse Last Layer.


  • ZZ F2L remains <RUL(D)>-gen.
  • Because of blockbuilding, solves can be very efficient.
  • Easier planning than EOLine makes it possible to plan more (e.g. XpEOLine) in inspection.


  • The Last Layer doesn't already have edges oriented, so 1LLL becomes less feasible.
  • Lots of regrips are needed during blockbuilding.
  • L/R switching requires regrips as well.
  • Blindspots can cause pauses to search for pieces.



EOSlice is the first step of ZZ-Slice. It is similar to EOLine and only differs in the position of the line edges, as DL and DR instead of DF and DB are solved.


  • F2, B2 and M moves can be used to make the solve more efficient, although exclusively <RULD>-gen solving is also possible.
  • ZZ F2L is solved in pairs, which allows for higher TPS than Blockbuilding
  • Regrips can be prevented by avoiding the use R2 and L2 moves.
  • The free M slice allows for an efficient L6EP finish.


  • Lack of blockbuilding makes ZZ F2L less efficient.
  • Due to unsolved pieces, blindspots exist in the back, which in turn hinder lookahead.
  • F2, B2 and M moves require regrips.
  • Pieces may get stuck in DF and DB.



EOLine was the original EO Step invented by Zbigniew Zborowski and solves a line of the DF and DB edges. It is followed by blockbuilding two blocks on L and R to solve F2L-1 + EO.

Even though it used to be the most common way to do ZZ, it has mostly been replaced by EOCross and is usually confined to One-Handed Solving.


  • The whole solve is fully <RUL(D)>-gen. (Although <RUF>-gen algorithms can be used for Last Layer.)
  • Because of blockbuilding, solves can be very efficient.


  • Lots of regrips are needed during blockbuilding.
  • L/R switching requires regrips as well.
  • Blindspots can cause pauses to search for pieces.



EOEdge (or Line On Left) is an EO step initially invented for MI2 and SSC, although it can be used in ZZ via ZZ-LOL. It is similar to EOLine, except that the line is made of the FL and BL edges rather than DF and DB.


  • ZZ F2L can be solved <RUD>-gen which is undisputably better than using R, U and L moves.
  • While regrips still exist, they aren't as bad as in EOLine.
  • Solving with EOEdge is as efficient as with EOLine.


  • Similarly to Cross on left, lookahead is enormously hindered, so searching for pieces and the resulting pauses are very common.


Partial EOArrow.png

pEOArrow or Partial EOArrow was proposed by Brayden Mossey and Alex Maass for the Hawaiian Kociemba method. Basically, you build cross minus one edge, a so called Mock Cross or "Arrow", and simultaneously orient only the F2L edges, like in pEOLine.


  • HKF2L is very neat as the edges are oriented and the DF edge is unsolved, which allows you to do tricks such as solving F2L cases using Roux techniques that preserve the DB edge.
  • Less regrips than in EOLine.
  • Planning pEOArrow is easier than EOArrow, which means that you can plan farther into the solve, for example up to XpEOArrow (pEOArrow + one pair).
  • Lower movecount than EOArrow, EOCross and EOLine.


  • Since the DF edge is solved, F2 moves or the M' U2 M trigger will be required during HKF2L.
  • The Last Layer doesn't already have all of its edges oriented.



EOArrow is an extension to pEOArrow which orients all edges. Although initially only used for Hawaiian Kociemba, it can also be applied to ZZ where it is the second most used EO Step for two-handed solving (after EOCross). In the variant for ZZ, one solves the arrow edges (usually DF, DL and DB or DF, DR and DB for left-handed people), followed by two F2L pairs on L (or R) and the right (or left) block. In Hawaiian Kociemba, the only difference is that the DR edge remains unsolved.

EOArrow can be seen as either a combination of EOLine and EOCross or EO applied to a Mock Cross.


  • Movecount is lower than in EOCross.
  • Less regrips than EOLine.
  • Most regrips are executed with the solver's dominant hand.
  • The solver needs to do less L/R switching than in e.g. EOLine and EOArrow.
  • Less blindspots than EOLine, especially when right block is being solved.
  • Right block can be solved fully <RU>-gen.
  • Due to the above, higher TPS can be reached than with EOLine.


  • Higher movecount than EOLine because of specified order.
  • More regrips than EOCross.
  • Harder to inspect than EOLine.



EOCross was invented when CFOP users applied the Cross to ZZ. So instead of only two D layer edges, all four are solved. The rest of the F2L is solved using CFOP-style F2L pairs. Nowadays, it is the most common way to do ZZ two-handed.


  • The Cross allows for almost regripless ZZ F2L.
  • Due to more pre-solved pieces, less blindspots exist.
  • Because of this, very high TPS can be reached.


  • Inspection becomes a lot harder and is comparable to that of an XCross.
  • Due to solving all D layer edges, ZZ F2L becomes 7 moves less efficient when compared with EOLine. [1]



With EO, a 2x2x2 block is solved. This is used in the WaterZZ method which was inspired by WaterRoux.

Since WaterZZ has a completely different approach to ZZ, it can't be compared with the other steps.



XEOLine (or also called XEOArrow) is when an EOLine and a 2x2x1 block (usually on L) are solved simultaneously. This is inspired by XCross and is a very advanced version of EOLine and EOArrow. The normal approach to continue the solve is to solve the remaining F2L pair on L and then a block on R.


  • If planned well, the movecount is significantly better than that of EOLine.
  • After the pair on L, no L/R switching is required.
  • The solve is finished <RU>-gen.
  • Regrips are reduced because of the already solved 2x2x1 block.
  • Most regrips are performed with the solver's dominant hand.


  • XEOLine is a lot harder to plan than normal EOLine and needs lots of time to master.
  • Like in EOArrow, some regrips still exist.



FBEO (or EOFB, not to be confused with the EOFB variant of EOLR) solves EO and First Block (a 1x2x3 block). It can be used in Roux and EOMR (a LEOR variant).


  • Very ergonomic (especially for One-Handed Solving because ZZ F2L can be finished using only R, U, r2 and M2 moves.
  • No L/R switching because of the movegroup.
  • Planning is slightly easier because centers can be an M2 off.


  • Very hard to plan all of it in inspection.
  • Regrips during the rest of the solve.



XEOCross is an extension of EOCross and XEOLine which solves all D layer edges and a 2x2x1 block in DBL (as opposed to only the D layer edges in EOCross and only line edges + 2x2x1 block in XEOLine). It could be compared to XXCross in difficulty.


  • The Cross allows for almost regripless ZZ F2L.
  • Due to lots of pre-solved pieces, almost no blindspots exist.
  • Since EO, Cross and first pair are solved simultaneously, this has a lower movecount than EOCross.
  • As only on pair on the left remains, less L/R switching exists (and could be completely removed by solving <RrUF(D)>-gen).
  • Because of the very good ergonomics, very high TPS can be reached.


  • Inspection becomes a lot harder and is comparable to that of an XXCross (2x2x3 block + edge).
  • While more efficient than EOCross, XEOCross is still less efficient than EOLine.



EO223 in one step (what Petrus achieves in three and LEOR in two) would be the ultimate EO Step. However, it seems pretty much impossible to plan it every time, although if it can be planned, the results usually are really good solves like Yusheng Du's 3.47 WR single.

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