Twisty puzzle device

Introducing the design of twisty puzzles. To successfully assemble our first twisty puzzle, we need to know what it is made of, how it rotates, and what its elements are called. What are twisty puzzles made of? Before we start putting together Platonic Solids puzzles, we need to make sure we know what pieces they are made of. This will help us intuitively understand how the pieces of twisty puzzles can move.

The twisting puzzle has the following elements:

Centers. They never change their position relative to each other and always remain in their place. Those. There will always be a pattern in the puzzle: opposite the white center there will be yellow, opposite the blue center there will be green, and opposite the red center there will be orange. The color of the center is, accordingly, the color of the assembled side (blue center ➝ blue side, etc.).

Edges. They have two colors and form a kind of “cross” when in place. These colors cannot be separated from each other.

Corner elements. They consist of 3 colors. These colors also cannot be separated from each other.

Faces. All the many elements that rotate around one axis or another are called puzzle faces. Moreover, the same elements (with the exception of centers) belong to several faces.

Notation (accepted in the WCA)

Algorithms will help us solve the cube. To write and read these algorithms, there is a certain form of recording the rotations of the puzzle faces. An apostrophe, or as speedcubers call it a “stroke,” means that the movement should be performed counterclockwise. To avoid confusion, imagine that you are looking at the rotating side directly in front of you. For example:

  • R (“right”) is the rotation of the right face clockwise.
  • R’ rotate the right face counterclockwise.
  • L (“left”) is the rotation of the left face clockwise.
  • L’ rotate the left face counterclockwise
  • D (“down”) is the rotation of the down face clockwise.
  • D’ rotate the down face counterclockwise
  • U (“up”) is the rotation of the up face clockwise.
  • U’ rotate the up face counterclockwise
  • F (“front”) is the rotation of the front face clockwise.
  • F’ rotate the front face counterclockwise
  • B (“back”) is the rotation of the back face clockwise.
  • B’ rotate the back face counterclockwise.

The number 2 after the letter indicates a rotation of 180°, for example: F2 U2′ D2 D2′, etc.

Rotate two layers at once.

Letter+w:
Fw – front face together with the middle layer clockwise,
Bw – back face together with the middle layer clockwise,
Lw – left side together with the middle layer clockwise,
Rw – right side together with the middle layer clockwise,
Uw – the top face together with the middle layer in a clockwise direction,
Dw – bottom edge together with the middle layer clockwise.

Everything is the same, but with a dash, indicating a counterclockwise turn:
Fw’ – front face together with the middle layer counterclockwise,
Bw’ – back face together with the middle layer counterclockwise,
Lw’ – left side together with the middle layer counterclockwise,
Rw’ – right side together with the middle layer counterclockwise,
Uw’ – the top face together with the middle layer counterclockwise,
Dw’ – the bottom face together with the middle layer counterclockwise.

A two after such a pair of letters indicates a double rotation of the corresponding face with the middle layer.
Fw2 – front face together with the middle layer at 180°,
Bw2 – back face together with the middle layer at 180°,
Lw2 – left side together with the middle layer at 180°,
Rw2 – right side together with the middle layer at 180°,
Uw2 – top face together with the middle layer at 180°,
Dw2 – bottom edge together with the middle layer at 180°.

Outer Block Moves (outer slice with adjacent inner slices). For each of the moves defined below, n is the total number of slices to move, which must be in the range 1 < n < N (where N is the number of layers in the puzzle). n may also be omitted, for an implicit value of n = 2 slices. Outer Block Moves are:

An important note why in WCA it is customary to denote the rotation of a face with an adjacent layer in this way: Previously, such movements (a face with a middle layer) in a 3x3x3 cube were denoted by small letters (r, l, b, d, u, f). But then large cubes appeared (4x4x4, 5x5x5, etc.) and due to confusion with the language of rotations of large cubes (there, small letters indicate rotations of only the internal layers), the World Cube Association (WCA) switched to the designations Rw, Lw, Fw and etc. Therefore, now we denote the rotation of any external face together with the internal layer adjacent to it with the index w.

Whole cube rotation.


It can be denoted in the same way as in standard notation or with small letters f, b, r, l, u, d in square brackets. The letters, as usual, indicate the edges from which you need to look at the moment of rotation.

Clockwise 90 degrees:

[f] or z – the entire cube rotates clockwise (view of the side of the front edge),
[b] or z’ – the entire cube rotates clockwise (rear view),
[r] or x – the whole cube rotates clockwise (view of the side of the right edge),
[l] or x’ – the entire cube rotates clockwise (left view),
[u] or y – the entire cube rotates clockwise (top view),
[d] or y’ – the entire cube rotates clockwise (bottom view).

Counterclockwise 90 degrees:

[f’] or z’,
[b’] or z,
[r’] or x’,
[l’] or x,
[u’] or y’,
[d’] or y.
As you probably noticed, the same rotation of the entire cube can be written in three ways:
[f] = [b’] = z.


Rotate 180 degrees:

[f2] or z2,
[b2] or z2,
[r2] or x2,
[l2] or x2,
[u2] or y2,
[d2] or y2.

Middle layers.


The WCA does not have special notation for mid-layer turns, but such turns are written using the notation already available. For example, the rotation of the middle layer located between the right and left edges clockwise, when viewed from the left edge (in standard notation, rotation “M”) can be written as Rw’R, or LwL’. This is the same thing, the first option is more convenient for right-handers, the second for left-handers. In competitions based on the number of moves, such a turn is, accordingly, counted as 2 moves.

Notation for Pyraminx:

Vertex rotation:

  • r left vertex clockwise.
  • r’ left vertex counterclockwise.
  • l right vertex clockwise.
  • l’ right vertex counterclockwise.
  • u up vertex clockwise.
  • u’ up vertex counterclockwise.
  • f back vertex clockwise.
  • f’ back vertex counterclockwise.

Face rotation:

  • R (“right”) is the rotation of the right face clockwise.
  • R’ rotate the right face counterclockwise.
  • L (“left”) is the rotation of the left face clockwise.
  • L’ rotate the left face counterclockwise.
  • U (“up”) is the rotation of the down face clockwise.
  • U’ rotate the down face counterclockwise.
  • F (“front”) is the rotation of the front face clockwise.
  • F’ rotate the front face counterclockwise.

Rotate two layers at once. Letter+w, for example:

  • rw left vertex clockwise and next layer.
  • Uw’ rotate the down face counterclockwise and next layer.

(for faces rotation only) to move multiple layers, add the layer number in front of the letter, for example:

  • 4Rw, where 4 is the number of layers to move.

Everything is the same, but with a dash, indicating a counterclockwise turn:

Notation for Megaminx:

Megaminx is a puzzle representing a regular dodecahedron, having 12 faces rotating at an angle of 72 degrees clockwise or counterclockwise (when rotating counterclockwise, add a «’» sign to the letter):

  • R (“right”) is the rotation of the right face.
  • L (“left”) is the rotation of the left face.
  • U (“up”) is the rotation of the up face.
  • D (“down”) is the rotation of the down face.
  • F (“front”) is the rotation of the front face.
  • B (“back”) is the rotation of the back face.
  • UR (“up right”) is the rotation of the up right face.
  • UL (“up left”) is the rotation of the up left face.
  • BR (“back right”) is the rotation of the back right face.
  • BL (“back left”) is the rotation of the back left face.
  • DR (“down right”) is the rotation of the down right face.
  • DL (“down left”) is the rotation of the down left face.

For double rotation (rotation by 144 degrees) after the letter designation we add «2» if rotation is clockwise and «2’» if rotation is counterclockwise.

The notation for rotating multiple layers is the same as in the cube notation.

Patterns on a twisty puzzle.
In addition to the usual assembly of six one-color faces of a Twisty Cube, this puzzle and its variants are used to obtain various patterns on them; the patterns themselves are called “solitaire”: “Chess Cube”, “Meson”, “Plummer Cross” and others.

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