Rubik's Cube Mechanics

Understanding the Cube

This page is about understanding the Rubik's Cube. If you want to be able to solve the Cube, talk about the Cube, or examine the Cube, it is necessary to understand - and be familiar with - its underlying mechanics, basic mathematics, and notation. There are too many people out there who try to solve the Cube but can't get anywhere because they do not take the time to look at it and understand how it works, and this page can teach you how to solve the Cube.

The Pieces of the Cube

The Rubik's Cube is made of 27 pieces. The stickers are each glued onto one specific piece, and they move around exactly as that piece does. Some pieces have more than one sticker on them; some only have one sticker. There are three kind of pieces: center pieces (marked 'N'), edge pieces ('E'), and corner pieces ('C').

First off, we will look at center pieces. The pieces labeled 'N' in the diagram are center pieces; there are six center pieces on a standard Rubik's Cube, each of which has a separate color (and just one sticker, of that color). It is important to note that center pieces are always in the same place relative to each other - they do not move around. It will always be possible, if red and yellow are next to each other on your cube, to hold the cube so that the red center is on top and the yellow center is at the front. These centers can rotate, but since they do not move they are the key to solving the Rubik's Cube. Colors that are on opposite (that is, not adjacent) centers are called opposing colors.

Next, let's look at edge pieces. There are twelve edge pieces on a Rubik's Cube, although you can only see nine (the 'E' pieces) in the diagram. Each edge piece has two stickers, of two adjacent colors. Two opposing colors can never be on the same edge. Notice with edges that, even if an edge is in the right place, it can be flipped and have the wrong orientation, so that the colors will be on the wrong sides. To solve an edge, it has to be in the right place and correctly flipped.

Finally, let's look at corner pieces (the 'C' pieces). There are eight corner pieces (one of which is hidden here). Each corner piece has three stickers on it, of differing colors, that represent three colors that are each adjacent to each other on the Cube. As with edges, no two opposing colors can ever be on the same corner. Since a corner has three possible orientations, it is quite likely for a center to be in the correct place but in the wrong orientation. To solve a corner, again, it must be in the right place and have the right orientation (or 'twist').

The pieces in a Rubik's Cube are organized into three layers (in each of three different directions). The vertical layers are often referred to as the lower layer (or first layer), middle layer (or second layer), and upper layer (or last layer).

Turns

The pieces on the Rubik's Cube are moved using turns. Each turn is a rotation, by a multiple of 90°, around one of the six center pieces. The centers are labeled relative to each other: F (Front), R (Right), U (Up), B (Back), L (Left), and D (Down). You have to memorize these names, and their relative positions. Unless you are writing down move sequences or solving the cube blindfolded, do not try to assign specific colors to labels, because if you rotate your cube the labels will move. The F face, for example, is always the face closest to you, and the U face is the uppermost face.

To scramble or solve the cube, you will use turns. A turn is represented in standard notation as the letter that you turn, plus a character that signifies the direction of the turn. If there is no character (R, for example) the turn is 90° clockwise; if the character is ' (R') the turn is 90° counterclockwise; and if the character is ² or 2 (R² or R2) the turn is 180° in either direction.

Perform a turn. Notice that a turn moves four corners and four edges in a cycle, as well as rotating a center piece. On most Rubik's Cubes, you will not have to take account of the centers' rotations, but in some cubes you will have to keep track of this. Turns of one outer layer do not move any centers, so all centers will stay in the same place. However, if you do a turn of two layers, or turn only a middle layer, you will move the centers. Note that the labels still keep their positions - moving the orange center around does not mean changing the location of any of the center labels.

Move Sequences

When you solve the cube or create patterns, you will be using specific sequences of moves that move pieces around. To describe the pieces, the convention is to describe every face that the piece is on. A piece that contains the same color as the U, F, and R centers is labeled 'UFR'. Note that a piece with one letter is a center, one with two letters is an edge, and one with three letters is a corner.

For more on move sequences, look at the commutator page.

The Cube as a Physical Object

Although the Rubik's Cube is often described as a mathematical construct - this is used whenever we talk about move sequences and turns, for example - it is also a physical object. This has a number of ramifications.

First, you can solve the Cube for speed, because you can learn to make turns very quickly. In fact, by doing something called 'fingertricks' (search other speedcubing sites...) you can perform more than one move at a time. This can speed up solving considerably.

Second, some Rubik's Cubes may squeak when turning or may be difficult to turn. In that case, putting some simple lubrication in the Cube can make it work more easily. The best lubrication to use is pure silicone, which can be bought as a spray; you can lubricate a Cube by spraying it into its inner workings. The worst lubrication is WD-40, which will literally dissolve most Cubes.

Finally, Cubes are subject to deterioration. So do not ever take the stickers off of a Cube, except if you are replacing them. If you do, the Cube will soon be in bad shape. It's way better to have an unsolved Cube than a ruined one. If your Cube falls apart often, you will have to either buy a new Cube or find some way of tightening the screws that hold the center pieces together. If your Cube's stickers are coming off, you will have to buy a new Cube or buy replacement stickers (which you can get at the official website.

Mechanics of Higher-Order Cubes

The 3x3x3 is not the only Rubik's Cube that you can buy. If you want, you can buy a 4x4x4 or 5x5x5 Cube, and larger ones may be on the market soon. But higher-order Cubes have issues that standard Cubes do not.

Larger Cubes, obviously, have more pieces, but they also have more turnable layers. In a 5x5x5 Cube, for example, each face has, not one, but two turnable layers, and that means that more complicated notations must be created.

Even Cubes can also have parity errors. Because the centers on even Cubes are not fixed, it is possible to flip a single edge (this cannot be done on a 3x3x3 cube) or switch two edges (which is also normally impossible). When solving, these parity errors can cause problems.

Finally, there is more than one center of each color on a higher-order Cube. The centers are interchangeable and it can be difficult to refer to them. I have yet to see an agreeable notation for higher-order Cube centers.