The top left corner and the top right corner of a face can change places. However, two edges change places when the moves for achieving this are over: the top middle edge and the bottom middle edge.
If you instead want to swap the top right and bottom right corners then you can do a set-up move: rotate the face so that those corners are at the top left and top right; then do the special swapping move; then rotate the face back to its original position.
In a similar way, you could swap the bottom two corners or swap the top left and bottom left corners.
It is the 'T Corners' move: the 'T' shape reminds me of the top left, top right, and the two edges which swap position.
If I use peg mnemonics to memorise the corners' position then I can visualise each corner as follows:
Note: The capital letters mean Green / Red / White / Yellow
Great Western Railway [a train image] (the G, W and R mean the corner with those three colours on).
GRimY [chimney sweep] (This is the corner with Green, Red and Yellow).
GuY Observing [with binoculars] (This is the corner with Green, Yellow and Orange).
GOWer peninsula [a sand castle image for the G,O,W stickers] (This is the corner with Green, Orange and Yellow)
It is useful to know the anti-clockwise or clockwise order of twisting corners. You can then think, "The current twisted corner needs two twists clockwise to reach the green dominant orientation: Great Western Railway. The three colours are in anticlockwise order. So, with the GWR piece, if its main sticker is white then one clockwise twist of it is needed to get it to show green dominantly.
At the blue face: the Clockwise order of the four corners is:
BeRry: Blue, Red, Yellow
Bus Wheels Rotate [a bus wheel for Blue, White and Red]
BOW (a person who has bowed)
Bring Your Own [vinyl] for Blue, Yellow, Orange
I listed the four green pieces as if the red face is the top face and I am staring at the green face; and the order is top left, top right, bottom right, bottom left.
If you were to turn the cube horizontally to reach the blue face (red face still the top face), I listed the four blue pieces in the order: top left, top right, bottom right, bottom left. Think of it as 1, 2, 3, 4 ideal positions of the corners at the green face and also at the blue face.
For a piece to be showing its correct final colour green at the green face, a corner may need twisting once or twice clockwise or it might already be showing the finished colour.
For a piece to be showing its correct final colour blue at the blue face, a corner may need twisting once or twice anti-clockwise or it might already be showing the finished colour.
By giving each twisted corner possibility a letter as its name, there can be 24 letters:
| Piece | Dominant Colour (in anti-clockwise order) | Letter |
| Great Western Railway [a train image] | G | A |
| W | B | |
| R | C | |
| GRimY [chimney sweep] | G | D |
| R | E | |
| Y | F | |
| GuY Observing [with binoculars] | G | G |
| Y | H | |
| O | I | |
| GOWer peninsula [a sand castle image] | G | J |
| O | K | |
| W | L | |
| BeRrY | B | M |
| R | N | |
| Y | O | |
| Bus Wheel Rotates | B | P |
| W | Q | |
| R | R | |
| BOW | B | S |
| O | T | |
| W | U | |
| Bring Your Own (Vinyl) | B | V |
| Y | W | |
| O | X |
The acrostic for remembering the first corner technique [T Corners move] is:
"Fortunately, none have nibbled biscuits produced in fields in contaminated paddocks."
The acrostic for remembering the other corner technique [Corner Twist move] is:
"Please Have Rotating Two Just Fine. Please Have Rotating Two Just Fine."
Considering the two corner techniques, the GWR order is useful left-to-right when figuring out which colour appears when the green corner travels from the blue face across to the green face; and when when considering the 'Corner Twist' move's effect on a corner.
You can make the same observation about the blue corner pieces.
The T move to switch corners between the green and blue face usually requires a set up of the green face by twisting it and of the blue face by twisting it so that the T shape appear; and then, after the manoeuvre, restoring the twisted face position.
One application of the 'T Corners' move is that, if all 4 green corners are at the green face but need swapping position with each other then you can use T Corner moves to fix that.
You may need to do many T moves to put corners where they belong. Sometimes, swapped edges (that I mentioned before) get swapped a second time so that, overall, it is as if they were never swapped around at all.
Here is a table of corner re-arrangements. I number the corners 1, 2, 3 and 4 as the top left, top right, bottom right and bottom left proper intended positions of the four corners:
"What Switches" will be letters like TBR meaning 'Top', 'Bottom', 'Right'. The top move and the bottom move cause edges to jump back to where they were. So the only edges change is the edges swapping when the Right side has a T Corners move done on it.
Desired order clockwise from the top left:
| Left Corners | Right Corners |
| 1 | 2 |
| 4 | 3 |
Eg. Where the instruction to solve it is just L then it means that the corners at the left side need to swap places: vertically change places.
| Start | --- | ---------- | What Switches |
| 3 | 1 | TBR | |
| 2 | 4 | ||
| 3 | 1 | TR | |
| 4 | 2 | ||
| 3 | 2 | LB | |
| 1 | 4 | ||
| 3 | 2 | RTR | |
| 4 | 1 | ||
| 3 | 4 | LRB | |
| 1 | 2 | ||
| 3 | 4 | RTBR | |
| 2 | 1 | ||
| 4 | 1 | LT | |
| 2 | 3 | ||
| 4 | 1 | LTR | |
| 3 | 2 | ||
| 4 | 2 | LRTR | |
| 3 | 1 | ||
| 4 | 2 | L | |
| 1 | 3 | ||
| 4 | 3 | LR | |
| 1 | 2 | ||
| 4 | 3 | LRT | |
| 2 | 1 | ||
| 1 | 2 | B | |
| 3 | 4 | ||
| 1 | 3 | R | |
| 4 | 2 | ||
| 1 | 3 | BR | |
| 2 | 4 | ||
| 1 | 4 | RBR | |
| 2 | 3 | ||
| 1 | 4 | RB | |
| 3 | 2 | ||
| 2 | 1 | TB | |
| 3 | 4 | ||
| 2 | 1 | T | |
| 4 | 3 | ||
| 2 | 3 | LBR | |
| 1 | 4 | ||
| 2 | 3 | RT | |
| 4 | 1 | ||
| 2 | 4 | TL | |
| 1 | 3 | ||
| 2 | 4 | RTB | |
| 3 | 1 |