Reflecting/Inverting/etc.. cubing algorithms in your head
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This tutorial is meant for people who are learning algorithms from a website where only one algorithm is given for a situation and you want to convert it to a different angle, or reflect it, or reflect it and convert it to a different angle, etc.. Below I list how I remember to do the conversions in my head. Using these techniques you don't have to rewrite the algorithms you are changing, but instead can just read it off and convert as you go.

I will of course assume in this article that you can read R L F B U D notation for the cube, and I will include the conversion instructions for the addition of M, E, S, x, y, z if you are familiar with this notation as well, however it is not necessary to know these extensions of the standard notation for this tutorial.

Algorithm Inversion How to do an algorithm backwards (set up a position)
Reflecting and Inverting across the RL plane
Reflecting and Inverting across the FB plane
Reflecting and Inverting across the UD plane

Many thanks to Lars Vandenbergh and Dan Harris for the use of imagecube.
Algorithm Inversion

In my opinion this should be obvious if you have already begun learning algorithms for the cube, but I include it for completeness.

To invert an algorithm, simply read it backwards and change the signs of all quarter turns. If a quarter turn is clockwise, change it to counter clockwise and vice versa.

Example 1:

Algorithm (as it will be given on an F2L page): (U2) R2 U2 R' U' R U' R2



To set up this position on a cube with the first two layers solved, you will have to do the inverse of the algorithm. Again, simply read the algorithm from right to left and change the sign of all quarter turns.

Inverting an algorithm goes from solvedto the case you want to set up

Original Algorithm: (U2) R2 U2 R' U' R U' R2
Inverse Algorithm: R2 U R' U R U2 R2 (U2)

Reflecting about the RL plane

This is the most common conversion used for cross on bottom users of the Fridrich method. This technique lets you read an algorithm given on a website so as to both set up and solve the reflection of that case (across the RL plane).

Algorithm reflection and inversion:

Basically all reflection and inversion means is that you want to know how to read the setup alg of the reflection (the inverse of the reflected algorithm). Any algorithm that you will be given on a website will always be the one that solves the case, however you now want to do the setup alg for the reflection. To do this simply read the alg backwards exactly as is, only interchange R <-> L. For an example see the algorithm below.

Example 2:

Algorithm (as it will be given on an F2L page): (U2) R2 U2 R' U' R U' R2



The reflected inverse of the alg goes from solvedto the reflection of the given case

Reflected inverse process: First read the given algorithm backwards, so start with the last R2. However, as you read backwards you have to also convert R's to L's and L's to R's. Lastly, remember not to change any turn directions, just interchange R <-> L.
Given algorithm: (U2) R2 U2 R' U' R U' R2
Reflected inverse: L2 U' L U' L' U2 L2 (U2)
*Note* if there are no R's or L's in your algorithm, just read it backwards.

Algorithm reflection

Now that you have the reflected case setup on your cube, you will now obviously want to be able to solve it. Below is how to convert the website's alg into the solution algorithm for the reflection.

Example 3:

Algorithm (as it will be given on an F2L page): (U2) R2 U2 R' U' R U' R2



The reflected alg goes from the reflected caseto solved

Reflection process: To reflect the given solution algorithm you have to read the normal direction (left to right). You also have to change the sign of all quarter turns. So if the turn is listed as a clockwise turn, you have to change it to a counterclockwise turn, and vice versa. Lastly you still have to interchange R <-> L, in addition to changing the sign if its a quarter turn. See below for the example.

Given algorithm: (U2) R2 U2 R' U' R U' R2
Reflected algorithm: (U2) L2 U2 L U L' U L2

Reflecting about the FB plane

This is another very common conversion used for cross on bottom users of the Fridrich method, as well as cross on right or cross on left solvers. This technique lets you read an algorithm given on a website so as to both set up and solve the reflection of that case (across the FB plane).

Algorithm reflection and inversion:

Basically all reflection and inversion means is that you want to know how to read the setup alg of the reflection (the inverse of the reflected algorithm). Any algorithm that you will be given on a website will always be the one that solves the case, however you now want to do the setup alg for the reflection. To do this simply read the alg backwards exactly as is, only interchange F <-> B. For an example see the algorithm below.

Example 4:

Algorithm (as it will be given on an F2L page): (U2) R2 U2 R' U' R U' R2



The reflected inverse of the alg goes from solvedto the reflection of the given case

Reflected inverse process: First read the given algorithm backwards, so start with the last R2. However, as you read backwards you have to also convert F's to B's and B's to F's. Lastly, remember not to change any turn directions, just interchange F <-> B.
Given algorithm: (U2) R2 U2 R' U' R U' R2
Reflected inverse: R2 U' R U' R' U2 R2 (U2)
*Note* if there are no F's or B's in your algorithm, just read it backwards.

Algorithm reflection

Now that you have the reflected case setup on your cube, you will now obviously want to be able to solve it. Below is how to convert the website's alg into the solution algorithm for the reflection.

Example 5:

Algorithm (as it will be given on an F2L page): (U2) R2 U2 R' U' R U' R2



The reflected alg goes from the reflected caseto solved

Reflection process: To reflect the given solution algorithm you have to read the normal direction (left to right). You also have to change the sign of all quarter turns. So if the turn is listed as a clockwise turn, you have to change it to a counterclockwise turn, and vice versa. Lastly you still have to interchange F <-> B, in addition to changing the sign if its a quarter turn. See below for the example.

Given algorithm: (U2) R2 U2 R' U' R U' R2
Reflected algorithm: (U2) R2 U2 R U R' U R2

Reflecting about the UD plane

Though I don't solve with cross on either right or left, I imagine this conversion would be rather useful for such a strategy. This technique lets you read an algorithm given on a website so as to both set up and solve the reflection of that case (across the UD plane).

Algorithm reflection and inversion:

Basically all reflection and inversion means is that you want to know how to read the setup alg of the reflection (the inverse of the reflected algorithm). Any algorithm that you will be given on a website will always be the one that solves the case, however you now want to do the setup alg for the reflection. To do this simply read the alg backwards exactly as is, only interchange U <-> D. For an example see the algorithm below.

Example 6:

Algorithm (as it will be given on an F2L page): (R2) U2 R2 U R U' R U2



The reflected inverse of the alg goes from solvedto the reflection of the given case

Reflected inverse process: First read the given algorithm backwards, so start with the last U2. However, as you read backwards you have to also convert U's to D's and D's to U's. Lastly, remember not to change any turn directions, just interchange U <-> D.
Given algorithm: (R2) U2 R2 U R U' R U2
Reflected inverse: D2 R D' R D R2 D2 (R2)
*Note* if there are no U's or D's in your algorithm, just read it backwards.

Algorithm reflection

Now that you have the reflected case setup on your cube, you will now obviously want to be able to solve it. Below is how to convert the website's alg into the solution algorithm for the reflection.

Example 7:

Algorithm (as it will be given on an F2L page): (R2) U2 R2 U R U' R U2



The reflected alg goes from the reflected caseto solved

Reflection process: To reflect the given solution algorithm you have to read the normal direction (left to right). You also have to change the sign of all quarter turns. So if the turn is listed as a clockwise turn, you have to change it to a counterclockwise turn, and vice versa. Lastly you still have to interchange U <-> D, in addition to changing the sign if its a quarter turn. See below for the example.

Given algorithm: (R2) U2 R2 U R U' R U2
Reflected algorithm: (R2) D2 R2 D' R' D R' D2

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