## Basic Cube Concepts

### Cube Structure

By studying the structure of a Rubik's cube you will get a greater understanding of how it works, something that will really help you solving the cube.

So, first of all, what actually is a classic Rubik's cube?

Rubik's cube is a cube with edges approximately 56 mm (2.2 in) long. It consists of 26 smaller cubes; one side is made up of 3x3 such cubes. If you take an ordinary cube and cut it as you would a Rubik's cube, you are left with 27 smaller cubes. Rubik's cube does not contain the cube from the very middle. In fact, the smaller pieces of the Rubik's cube does not really have a shape of a cube. We call these 26 small pieces cubies.

There are 6 cubies in the middle of individual sides, and those are rigidly interconnected by a six-armed spatial cross (they merely rotate around their axles and keep other cubies from falling off the cube). I will call those cubies centers. The centers are connected to the cross by means of screws and springs, causing other cubies to hold nicely tightly together. Each of the center cubies has one colored sticker on its external side, which determines the color of each cube face. The colors are usually white, red, blue, yellow, orange, and green. Sometimes brownish color replaces red color. The original Rubik's cube (as well as all of the recently produced Rubik-brand cubes) has coloring white opposite yellow, red opposite orange, and blue opposite green. Yet another coloring, (widespread in America and Japan) exists: white opposite blue, red opposite orange, and green opposite yellow. The former coloring has a certain logic, called "plus yellow", because opposite side of one color (white, red, or blue) is formed by adding yellow color (yellow, orange, or green). On the other hand, the latter coloring tries to combine opposite sides with maximum contrast. Each coloring can further have two variants due to a mirror reflection.

We also have 12 edge cubies, or just edges. Those cubies have two stickers of different colors.

And the last type of cubies are eight corner cubies, or just corners. Those cubies have three differently-colored stickers on their mutually orthogonal sides.

### Labelling of Moves

As you surely know, the Rubik's cube has 6 sides. All sides can be rotated by a certain angle. This rotation is called a move (or a turn).

In order to be able to perform other moves, it is recommended to rotate by 0 (360), 90, 180, or -90 (270) degrees. The 90 and -90 degrees turns are called quarter turns. The 180 degreed turn is called a double turn (or sometimes - a bit misleading - face turn is used). Of course, if you rotate a side, you rotate one third of the cube (9 cubies). This array is called a layer.

Having a cube in front of you, the individual layers are rotated thus:

• A layer facing towards you is the front layer, and is labelled as ` F ` (Front).
• A layer facing away from you is the back layer and is labelld as ` B ` (Back).
• A layer which is on top is the up layer and is labelled as ` U ` (Up).
• A layer which is at bottom is the down layer and is labelled as ` D ` (Down).
• A layer which is on your right is the right layer and is labelled as ` R ` (Right).
• A layer which is on your left is the left layer and is labelled as ` L ` (Left).
• A layer which is between the left and right layer is labelled as ` M ` (Middle).
• A layer which is between the top and bottom layer is labelled as ` E ` (Equator).
• A layer which is between the front and back layer is labelled as ` S ` (Standing).

The move is labelled by the symbol of the layer you are turning (F, B, U, D, L, R). A symbol by itself labels a clockwise rotation of the layer. For a counterclockwise rotation, the layer symbol is followed by an apostrophe (a single quote}. For a 180-degree rotation, the layer symbol is followed by digit '2' or an exponent "to the second power." There are other ways of labelling the moves, but this one is the simplest and most widely used (it is so-called "Singmaster notation" after a mathematician who published it).

Turning M, E, and S layers is called slice turn. For M turn the direction is top-down, for M' bottom-up. For E turn the direction is left-rigth, for E' rigth-left. For S turn the direction is clockwise if seeing from front, for S' couterclockwise.

For a clearer understanding here is an example:

For example ` F2 U' R M' ` means: Rotate the front layer by a half-turn (180 degrees in any direction), then rotate the up layer counterclockwise by a quarter-turn (90 degrees), then rotate the right layer clockwise by a quarter-turn (90 degrees) and finally rotate the middle layer in a bottom-up direction by a quarter-turn.

On some pages (especially for beginners) we use a graphical notation that may be easier to follow at first. For example ` F2 U' R M' ` would be written as:

All displayed turns are only the quarter ones. Double turns are decomposed to a sequence of two quarter turns of the same layer to reduce complexity.

It is worth noting, that you turn each side in a given direction, if the side is facing you (you don't need to pivot the whole cube, but rotate the side in the same direction you would rotate, if the side was facing you). It may not be completely clear at first, but it is sufficient, if you turn the cube so that the side to be manipulated is facing you, execute the move, and then turn the cube back to its original position.

Sometimes we will talk about correctly positioned corners/edges, correctly oriented corners/edges. A correctly positioned cubie is a corner or edge cubie that is at the right place on the cube relative to its centers regardles how it is twisted in this position. Correctly oriented corner or edge is further twisted so that the sticker of a given color is adjacent to the sticker of the center cubie of the same color. A corner may be at the same place in three different orientations (oriented, twisted clockwise, and twisted counter-clockwise). An edge may be at the same place in two different orientations (oriented and flipped).

Certain corners and edges will be specified either by their colors (e. g. white-blue edge) or by their placement in the picture (e.g. UL edge) for edge common to the up and left layer.