To create any patterns on the cube, it must be assembled
Let the orientation of the cube be as follows: top – green, front (facade) – white, right side – red, bottom – blue, back – yellow, left side – orange.

“Points” – also called “6 points”. Formula: Bw B’ Lw’ L Bw’ B Lw L’.
“Donkey bridge” (second order chess cube). Formula: Lw2 L2 Dw2 D2 Bw2 B2.
Donkey Bridge with Dots is a combination of the two previous solitaire games. Formula: (Lw2 L2 Dw2 D2 Bw2 B2) + (Bw B’ Lw’ L Bw’ B Lw L’)
“Zigzag” Formula: ( R L F B )3, which is equivalent to this entry: (R L F B) (R L F B) (R L F B).
Four “Z’s”. Add to Zigzag ( U2 D2 ) and you get four “Zs”. Formula: (R L F B)3 (U2 D2).
“Globe” – a figure invented by D. Maxwell, is a “globe” on which 54 countries are located, and none of them touches the extended borders of a country that matches the color on the globe. Formula: (F B L R) (F B L R) L R.
Plummer’s Cross. Formula: D2 Lw2 L2 D Lw2 L2 D2 Bw2 B2 U’ Bw2 B2 L2 Dw2 D2 L Dw2 D2 L2 Bw2 B2 R’ Bw2 B2, and one: B F2 D’ R2 F D B’ F D’ U F’ D’ L2 F D2 U’. Both formulas lead to the same result, although the second is shorter, the first is easier to remember.
Christman’s Cross. Formula: R’ ( Lw2 L2 Bw2 B2 U2 Lw2 L2 Bw2 B2 D2) R.
Chess cube of the 3rd order. This shape is a combination of the Plummer Cross and Dot shapes. Formula: R2 Dw2 D2 R Dw2 D2 R2 Bw2 B2 L’ Bw2 B2 U2 Lw2 L2 U Lw2 L2 U2 Bw2 B2 D’ Bw2 B2 Lw’ L Bw B’ Lw L’ Bw’ B.
Chess cube of the sixth order. A combination of 3rd order chess cube and Donkey Bridge algorithms. Formula: R2 Dw2 D2 R Dw2 D2 R2 Bw2 B2 L’ Bw2 B2 U2 Lw2 L2 U Lw2 L2 U2 Bw2 B2 D’ Bw2 B2 Lw’ L Bw B’ Lw L’ Bw’ B Bw2 B2 Dw2 D2 Lw2 L2.
Figure 6H: Formula: D2 Lw’ L Bw2 B2 Lw L’ U2.
Figure “6 minuses”. Formula: R2 F2 Lw2 L2 B2 L2 Lw’ L.
“Two inverted diagonal corner posts” Formula: F ( L D2 R’ D) L2 (D’ R D2 L’) F (L2 F2).
“Two corner posts on one side” – let’s continue building different posts. Formula: R2 (F D R2 D’ R) B2 (R’ D R2 D’ F’) (R2 B2).
“Columns with a cross” – let’s perform the previous algorithm, rotate the cube 180 degrees around the vertical axis and repeat the same algorithm again. Formula: (R2 F D R2 D’ R B2 R’ D R2 D’ F’) (R2 B2) (L2 B D L2 D’ L F2 L’ D L2 D’ B’ L2 F2).
“Columns with a checkerboard cross” – in the previous algorithm, replace the last bracket (L2 F2) with (R2 B2): Formula: (R2 F D R2 D’ R B2 R’ D R2 D’ F’) (R2 B2) (L2 B D L2 D’ L F2 L’ D L2 D’ B’ R2 B2).
“Columns with a roof” – add to the previous algorithm (Lw2 L2 Bw2 B2) Formula: (R2 F D R2 D’ R B2 R’ D R2 D’ F’) (R2 B2) (L2 B D L2 D’ L F2 L’ D L2 D’ B’ R2 B2) (Lw2 L2 Bw2 B2).
Four U’s Formula: Lw2 L2 U Lw2 L2 U2 Lw2 L2 D Bw2 B2 Dw D’.
Four “T” – Previous pattern (“4 U”) + D2. Formula: Lw2 L2 U Lw2 L2 U2 Lw2 L2 D Bw2 B2 Dw D’ D2.
“4 double inverted Ls and 2 double Ls” Formula: L’ R’ U D L R U’ D’ F’ B’ U D.
Solitaire “BDT” – large diagonal triangle. Formula: R U F’ D2 F U’ F’ D2 F R’. or: R’ U B2 U’ F’ U B2 U’ F R.
Solitaire “BBT” – large side triangle: Formula: F’ Dw’ D R U2 R’ Dw D’ R U2 R’ F.
This is also a BBT, only with a different arrangement of cubes. R Dw D’ F’ U2 F Dw’ D F’ U2 F R’ – a formula that is mirror to the previous one (as if a mirror was placed to the right or left of the cube and the moves were recorded).
“Worm.” It’s not very clear from the image why it is called that, but when you assemble this pattern and spin the cube, everything will become clear. Until then, let there be intrigue. Formula: U B2 L D B’ F L’ D U’ L’ R F’ D2 R’.
“6 letters T” – option one. I would call this algorithm simply “second order letters”. Formula: U2 R2 F2 D’ U B2 L2 D’ U’. If you repeat this formula 2 times in a row without changing the position of the cube, you will get 6 characters “:”, 3 times – 6 letters “H”, 4 times – again 6 characters “:” (only with the legs in the other direction), 5 times – 6 letters “C”, 6 times – the cube will be solved.
The “6 T” pattern is also letters of the second order – the second option, with a different arrangement of letters. Formula: B2 D2 L R’ D2 B2 L R’. By repeating this algorithm 2 times you will get 6 characters “:”, 3 times – 6 letters “H”, 4 times – again characters “:”  (the side letters will turn in other directions), 5 times – 4 letters “T” and 2 letters “C”, after the sixth time the cube will be solved.
“MBT” – small side triangle. Rearranging three side cubes on adjacent faces. Formula: R’ D U2 B Dw D’ B2 Dw’ D B D’ U2 R. The reverse sequence of actions will rearrange the cubes in the opposite direction: Formula: R’ U2 D B’ Dw D’ B2 Dw’ D B’ U2 D’ R. You can do it differently. If in the first formula we change the direction of movement of the back face to the opposite, then the cubes will also be rearranged in the other direction: R’ D U2 B’ Dw D’ B2 Dw’ D B’ D’ U2 R.
“Meson” (“quark – antiquark”) – (B’ T2 B L’ F2 L)2. This formula is the shortest of all that I have come across for this pattern. (U’ B2 U L’ F2 L) (U’ B2 U L’ F2 L), The reverse formula rotates the cubes in the other direction: (L’ F2 L U’ B2 U) (L’ F2 L U’ B2 U), You can turn the cubes in the other direction using these formulas: (R’ D2 R B’ U2 B) (R’ D2 R B’ U2 B), (D’ R2 D F’ L2 F) (D’ R2 D F’ L2 F).
“Giant meson” – a cube within a cube. The small cube remains in place, the outer edges “rotate” around it. Formula: (F’ U’ B U2 B’ U R U2 R’ F) (B D F’ D2 F D’ L’ D2 L B’), (B L’ D2 L D F’ D2 F D’ B’) (F’ R U2 R’ U’ B U2 B’ U F) – The reverse sequence of actions will lead to the opposite result, that is, it will “turn” the colors in the opposite direction. By the way, note that the formula is divided into 2 parts, and the sequence of commands in brackets is suspiciously similar, but different. The turns in them are mirrored along all three planes, that is, turning the top face clockwise became a turn of the bottom counterclockwise, the façade counterclockwise became a turn of the back face clockwise, turns of the right side became turns to the left with a change in the direction of rotation, a turn of 180 degrees became such and remains, but on the opposite side. By the way, it is not forbidden to swap the brackets; the result will still be the same, since they contain independent algorithms, each of which rearranges 3 pairs of adjacent cubes in a circle. Here are two more formulas (one “there”, the other “here”) that will lead to the same results as the previous two. And they are similar to the first ones, like twin brothers, only they arrange pairs of cubes differently: (L’ B D2 B’ D’ R D2 R’ D L) (R F’ U2 F U L’ U2 L U’ R’), (R U L’ U2 L U’ F’ U2 F R’) (L’ D’ R D2 R’ D B D2 B’ L). The same results are achieved with the following pair of formulas: Formula: (U L2) D (R B’) (R B’) (R B’) D’ (L2 U) (R2 F2 U2), Formula: (U2 F2 R2) (U’ L2) D (B R’) (B R’) (B R’) D’ (L2 U’). If any of these formulas is repeated 3 times, then the Rubik’s cube will return to its original state, that is, it will be solved.
“Giant meson with cherries” – A cube in a cube, which is again in a cube. Formula: R U’ L F U’ R2 U2 R U R’ U2 D’ L D F2 L2 U. The formula, inverse to the previous one, “rotates” the colors in the other direction: U’ L2 F2 D’ L’ D U2 R U’ R’ U2 R2 U F’ L’ U R’. The same results can be achieved by a combination of patterns already known to us – “giant meson” and “just meson”, taking into account the direction of “rotation” of the colors. That is, the small cube should rotate in the direction opposite to the rotation of the “external” colors. Formula: (F’ U’ B U2 B’ U R U2 R’ F) (B D F’ D2 F D’ L’ D2 L B’) (L’ F2 L U’ B2 U) (L’ F2 L U’ B2 U). Reversed: (B L’ D2 L D F’ D2 F D’ B’) (F’ R U2 R’ U’ B U2 B’ U F) (U’ B2 U L’ F2 L) (U’ B2 U L’ F2 L). If the direction of rotation of the small cube and the outer colors coincide, you will get another pattern – “Rings”.
“Rings” of the third order. In this case, as you understand, this is a combination of a “giant meson” and simply a “meson”. Formula: (F’ U’ B U2 B’ U R U2 R’ F) (B D F’ D2 F D’ L’ D2 L B’) (U’ B2 U L’ F2 L) (U’ B2 U L’ F2 L). A shorter formula will lead to the same result: F2 D’ R2 D’ L’ U’ L’ R B D’ U B L F2 L U2. The reverse sequence of actions will “turn” the colors in the other direction. But that is not all. Rings can be “assembled” from other solitaire games – from the “points” and “MBT” known to us – the small side triangle: (R’ D U2 B Dw D’ B2 Dw’ D B D’ U2 R) (L’ B2 F U’ Bw’ B U2 Bw B’ U’ B2 F’ L) (Bw B’ Lw’ L Bw’ B Lw L’), (R’ D U2 B Dw D’ B2 Dw’ D B D’ U2 R) (L’ F B2 U’ Bw’ B U2 Bw B’ U’ F’ B2 L) (Bw B’ Lw’ L Bw’ B Lw L’), (R’ D U2 B Dw  D’ B2 Dw’ D B D’ U2 R) (L U’ D2 F’ Dw D’ F2 Dw’ D F’ U D2 L’) (Bw B’ Lw’ L Bw’ B Lw L’). A short explanation of these three formulas. They all lead to the same result. The first of them uses the direct and inverse “MBT” formulas. In the second formula in the second bracket, only the direction of rotation of the back face is changed. In the third formula, the second “MBT” is inverted for the opposite corner of the cube, so as not to once again rotate the Rubik’s cube. It is not difficult to guess that with the help of “MBT”, “Dots” and a simple “Meson”, taking into account its rotation, you can “collect” the two previous solitaire games – “Giant Meson” and “Giant Meson with Cherries”. That is, adding “Meson” to the last formulas of “Rings”, in one direction or another, we get either “Giant Meson” or “Giant Meson with Cherries”.
“Otherworldly rings” – rings of the second order: Formula: R’ F2 U2 R2 B’ L2 D’ B2 R’ B2 L2 B R2 U’ R2. The reverse sequence of actions will lead to exactly the same result, that is, the same pairs of faces will “exchange” the same colors. Therefore, which option is easier for you to remember, decide for yourself. Here is another formula with exactly the same result: (R F B’ D’) F2 (D B F’ R’) F2 (U R2 U’) (D R2 F B U2 B’ F’ R2 D’). If in this formula you replace the last bracket with (D F2 D’), you will get a different pattern on the Rubik’s cube – “Snake”.
“Snake”: in the previous operation, replace the fourth (large) parenthesis with (D F2 D’), it will look like this: (R F B’ D’) F2 (D B F’ R’) F2 (U R2 U’) (D F2 D’) .
“Otherworldly Meson Rings.” As you might guess, you can create such a pattern by combining two others – “meson” and “otherworldly rings”. All the formulas needed for such solitaire are already in our arsenal. For example like this: (R’ F2 U2 R2 B’ L2 D’ B2 R’ B2 L2 B R2 U’ R2) (L’ F2 L U’ B2 U) (L’ F2 L U’ B2 U). I’ll give here another formula for this solitaire game, it’s shorter: R’ Bw2 B2 D2 Bw2 B R L2 B D’ B D B2 D B2 L’ D L’.
“6 flags”. The idea behind the pattern is that each side is made up of stripes of three different colors. If, for example, on one side a blue stripe is adjacent to yellow and white, then on no other side will it appear with stripes of these colors. Formula: U’ B2 L2 U Lw2 L2 U’ R2 F2 D F B R Dw D’ R’ B’ R’ Dw D’ R2 Dw’ D R’ F’ B2 R2 B2 F2 Bw’ B.
“Fish” Formula: U F2 U’ B’ U2 B U’ F2 U’ R’ U2 B’ U2 B R.
“Second-order corners” are “otherworldly” (by analogy with rings) corners. Formula: F2 R2 D R2 D U F2 D’ R’ D’ F L2 F’ D R U’.
“Third-order corners” – it would be possible to assemble such a pattern using a combination of the “MBT” and “meson” algorithms, but there is a shorter formula: Formula: U L2 D F D’ B’ U L’ B2 U2 F U’ F’ U2 B’ U’.
“Cherry of the second strand” (Otherworldly cherries): Formula: F’ D L2 U’ R B L2 F’ D F U’ F’ L’ B D L F’.
“Third-order cherries” – can be collected using “meson” and “points”, or you can do this: Formula: D F2 U’ B F’ L R’ D L2 U’ B R2 B’ U L2 U’.
“Escher” – probably in honor of the Dutch artist Maurice Cornelius Escher, but in general, it looks more like a propeller: Formula: U F2 D2 R2 U’ L B2 R F D F R F’ D’ L2 U2.
“Screw” reminds me more of “triple hooks” or shuriken. Formula: U’ L2 U2 R2 U’ B2 L’ B D R’ B’ L’ B’ D2 B’ L D B’ U’.
“Second-order rocket”. Formula: D U L2 B2 D U’ F’ U F’ R F2 R’ F D’ B2 L2 D’ U’.
“Third-order rocket” – something tells me that it can be assembled like a “worm” with a “meson”, but “we will go the other way”, in short: Formula: B2 U L2 R2 D’ F’ D’ R U F2 L2 U L’ D2 L R B’ U.
“Reverse” – All side cubes are reversed in their places. The solution to this solitaire game was found using the program “Cube Explorer 5.12” by Herbert Kociemba, a mathematician from the University of Darmstadt (Germany). Here, in fact, is the algorithm for this solitaire game: U R U2 R F2 L U2 R F’ B’ R2 D R’ L U2 F2 D2 F R2 D. And one more: F B R2 U R’ L U2 F2 D2 B R2 U’ D’ R F2 L U2 R F2 R. and two more a little more authentic: R L F U2 R2 U’ D’ F2 R’ F B U L2 B2 D2 R2 D’ L2 D B2 D, U D R F B’ U2 R2 U R L’ F L2 U2 B2 L2 F L2 F’ R2 L2 F L2. The direct and reverse sequence of any of the above algorithms for this solitaire game will lead to the same result – the reversal of all edge cubes in their places.
“Three-color diagonal”, even as many as six diagonals: Formula: D2 U B2 U2 B2 L2 B2 D F’ L’ U’ F2 D2 F D B’ L F U’.
6 letters “U” with legs facing outwards. I will give several different algorithms. How are they different? Firstly, the arrangement of letters on the cube, secondly, the direction of movement of the cubes during the execution of the algorithm, and thirdly, the sequence of operations. So, the first group of formulas is a combination of two algorithms given earlier on this page – “BDT” and “points”. The letters “U” are located with their legs facing outward in a clockwise direction. The centers move counterclockwise: (R Dw D’ F’ U2 F Dw’ D F’ U2 F R’) (Dw D’ Bw’ B Dw’ D Bw B’). The inverse formula moves the centers clockwise: (R F’ U2 F Dw D’ F’ U2 F Dw’ D R’) (Bw’ B Dw D’ Bw B’ Dw’ D). If we invert these two formulas, so to speak, reflect them diagonally passing through the far left corner and the near right corner, then the letters U will be located with their legs outward, but counterclockwise, and the centers will change the direction of rotation to the opposite. The letters “U” are located with their legs facing out counterclockwise. The centers move clockwise (inversion of the first formula): (F’ Dw’ D R U2 R’ Dw D’ R U2 R’ F) (Bw’ B Dw D’ Bw B’ Dw’ D). The inverse formula moves the centers counterclockwise (inverse of the second formula): (F’ R U2 R’ Dw’ D R U2 R’ Dw D’ F) (Dw D’ Bw’ B Dw’ D Bw B’). The inverse formulas here are not exactly inverse, but since each of the two parts of these formulas is an independent algorithm with cyclic movements of the cubes, the combination of inverse algorithms leads to the same result as if the entire formula were reproduced in reverse (rearrange the parentheses in the inverse formulas, and they will become completely reverse). Repeating any of these algorithms three times solves the cube again. Here is another group of four formulas that will lead to the same results as the 4 formulas above. This is also a combination of “BDT” and “dots” in other versions. “U” legs outward clockwise, centers move counterclockwise: (L’ R’ R’ F’ L’ B’ U B L F R U’ R L) (R L’ F B’ U D’ R L’) = (L’ R’ R’ F’ L’ B’ U B L F R U’ R L) (Lw L’ Dw’ D Lw’ L Dw D’). “U” with legs outward clockwise, centers move clockwise: (L’ R’ U R’ F’ L’ B’ U’ B L F R R L) (Dw’ D Lw L’ Dw D’ Lw’ L). “U” with legs outward counterclockwise, centers move clockwise: (B F F R B L U’ L’ B’ R’ F’ U F’ B’) (Dw’ D Lw L’ Dw D’ Lw’ L). “U” with legs outward counterclockwise, centers move counterclockwise: (B F U’ F R B L U L’ B’ R’ F’ F’ B’) (Lw L’ Dw’ D Lw’ L Dw D’). Another set of formulas on the topic 6 “U”. “U” with legs outward clockwise, centers move counterclockwise: D Lw L’ U’ L’ D Bw B’ D’ L Dw D’. “U” with legs outward clockwise, centers move clockwise: Dw’ D L’ D Bw’ B D’ L U Lw’ L D’. “U” with legs outward counterclockwise, centers move clockwise: D’ Lw’ L U L D’ Bw B’ D L’ Dw’ D. “U” with legs outward counterclockwise, centers move counterclockwise: D’ U B D’ L’ R F D’ B’ D’ U L.

6 letters “U” with legs inward (toward each other) – option 4, the trickiest – the centers remain in place. “U” with its legs inward counterclockwise, the letters moved clockwise:
U R2 B Lw’ L B’ L’ R’ B’ D’ F’ Lw L’ F U .

The reverse formula will rotate the letters with their legs clockwise and move them counterclockwise:

U’ F’ Lw’ L F D B R L B Lw L’ B’ R2 U’.
What else is interesting about this algorithm? When performing it, the corner cube (on the projection it is in the center) and the outer “ring” of cubes rotate in one direction, and the middle “ring”, with the exception of the central cubes on the faces, that is, the edge cubes in this ring, rotate in the opposite direction.
Therefore, if you repeat this algorithm 2, 3 and 4 times in a row, you will get 3 more such patterns on the Rubik’s cube. The result of 5 repetitions is equivalent to the result of the inverse formula; 6 repetitions will return the cube to its original (assembled) state. I think there are now more than enough algorithms with the letter “U” and their derivatives.

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