A Rubik’s turn is just colors chasing each other around a loop.

Ignore the plastic cube for a second. Watch the thick colored loop on the dots.

What the picture is saying

Stickers are dots. There are 54 of them, in six blobs of nine.
A turn is a slide along a loop. The colors walk. The dots stay where they are.
Solved means each blob is one color. Nine white dots together, nine red, and the same for the rest.
Spinning the whole cube only changes where you look. The dots do not change.

One blob of nine dots. The middle one stays. The others can walk a loop.

For grown-ups

The next part uses math names for the same idea.

Permutations

A quarter turn is a bijection of the 54 slots. Doing U and then R is composition, and order matters: U then R is not R then U.

The move tables on this page are the clockwise face turns in Kociemba’s “carried to” numbering: slot i is sent to the slot named by the table.

Cycles

Write that bijection in disjoint cycles. Clockwise U is five 4-cycles. Centers are 1-cycles, so they do not appear. Four clockwise turns of the same face bring every sticker home.

The thick arcs are those cycles. A traveling dot is one sticker walking one step of its cycle.

The cube group, on facelets

The legal turns generate a group. That group acts on the set of 54 facelets: every position is some permutation of the stickers.

This page draws that action. The vertices are stickers, not positions of the whole cube.

What a gray edge is

Take each generator — U, R, F, D, L, B — and forget direction. If a generator sends slot i to slot j, draw the edge {i, j}.

The gray graph is the union of those edges. It is static. A center has degree zero: no face turn moves it.

Conjugacy, lightly

The algorithm U R U′ means: turn the top, turn the right, undo the top. As a permutation of slots that is U′ ∘ R ∘ U.

It is the same cycle type as R, transported onto the slots where U′ drops it. The gold arcs after the fancy turn are that conjugate.

Another graph, not this picture

There is a second famous cube graph. Its vertices are reachable states of the whole cube, and a turn is a step from one state to a neighbor. Solvers search that graph. It is not the drawing of the dots.

43,252,003,274,489,856,000 vertices

8! · 3⁸ · 12! · 2¹² / 12

	This page	Configuration graph
Vertices	54 sticker slots	Every reachable cube state
Edges	A quarter turn can carry a sticker from one slot to the other	One face turn takes one state to another
When you scramble	Colors move. The drawing does not.	You walk to another vertex.
God’s number	Not a distance in this graph	20 in half-turn metric, 26 in quarter-turn metric

In the half-turn metric a 180° turn counts as one move, and every position can be solved in at most 20. In the quarter-turn metric a 180° turn counts as two, and the maximum is 26. Those bounds were proved by computer search (half-turn metric in 2010, quarter-turn metric in 2014).

Rewind on this page does not look through that graph. It takes the turns you already made and plays their inverses from the end of the list back to the start.