What is this page?

These are algorithms for the first step of the ortega method. This step involves building a single face. Normally, you solve this step intuitively, not with algorithms. As such, I do not recommend actually learning these algorithms. They are just to give you ideas as to how some cases can be solved optimally, to help make your intuitive solutions a little more efficient.

I think this list of cases is complete, but I worked them out manually, so I'm not really sure.

If the diagrams aren't obvious,here is an explanation. Each face assumes that you turn the cube to look directly at that face. The topmost part is the top face. On the middle row you have the front, right, and back faces. Finally the bottom face is depicted on the bottom. The left face is not depicted in the diagrams because it wasn't really necessary.

You always want to start with a face that has at least two pieces already in position (you MUST be color neutral for this to work every time). Put this on the bottom side. You may need to ajust the U face in order to match the diagrams. The numbers after the algorithms are the move count, first with half-turn metric, and then with quarter-turn metric.

For each case, I have provided both the shortest solutions, as well as longer ones that may be easier to execute. Cases 1-33 have 2-gen algs available, but cases 34-50 do not (as far as I could tell).

1 1
FRF'R' (4,4)
R'F'UF (4,4)
R'URUR' (5,5)
RURU'R2 (5,6)
R2U'RUR (5,6)
2 2

FRU'R' (4,4)
R'F'RF (4,4)
FU'F'U'F (5,5)
F'U'F'UF2 (5,6)
F2UF'U'F' (5,6)

3 3 F'U'F (3,3)
URU'R' (4,4)
R'FRF' (4,4)
U2RU2R' (4,6)
4 4 RUR' (3,3)
5 5 UR2U'R2 (4,6)
U'F2UF2 (4,6)
6 6 RU'RU'R (5,5)
RF2R'U'R' (5,6)
R'U'RU2R' (5,6)
R'U2RU'R' (5,6)
7 7 RF2U'R2 (4,6)
R'F2UF2 (4,6)
RU2R2UR2 (5,8)
R'U2R2U'R2 (5,8)
8 8

R2F'RF (4,5)
R'FRU'R' (5,5)
UR'U'RUR' (6,6)
U2R'U2RUR' (6,8)

9 9 URU'R2 (4,5)
R2F'UF (4,5)
10 10
R'F2R2F (4,6)
RF2R2F' (4,6)
RU'R2UR' (5,6)
R'UR2U'R (5,6)
R2UR2U2R (5,8)
R2U'R2U2R' (5,8)
11 11 R'UR'UR' (5,5)
RUR'U2R (5,6)
RU2R'UR (5,6)
12 12

FU'R' (3,3)
U2RU'R2U'R' (6,8)

13 13 F2R2F' (3,5)
U'R2UR' (4,5)
R2F2R2F (4,7)
14 14 UFU'R' (4,4)
U'RU'R2U'R' (6,7)
15 15 R2UR' (3,4)
16 16 U'RU'R (4,4)
F2R'U'R' (4,5)
17 17 R2U'R (3,4)
18 18

U'F'RF (4,4)
RUFU'R' (5,5)
R'UFU'R' (5,5)
UR'U2R2U'R' (6,8)

19 19 F2R2F (3,5)
UR2U'R (4,5)
R2F2R2F' (4,7)
20 20 R'UR' (3,3)
21 21 RUR'UR' (5,5)
R'U'FRF' (5,5)
R'UR'U2R (5,6)
R'U2R'UR (5,6)
22 22 RF2UF2 (4,6)
R'F2U'R2 (4,6)
RU2R2U'R2 (5,8)
R'U2R2UR2 (5,8)
23 23 R'UR'U'R (5,5)
FU'R2F'R (5,6)
R'U'FR2F' (5,6)
R'U2FR'F' (5,6)
24 24 UR'U'R' (4,4)
R'FR'F' (4,4)
25 25 RUR2 (3,4)
26 26 U'RF'RF (5,5)
F'R2U2RF' (5,7)
R'UR2UR2 (5,7)
R'U'F2U'R2 (5,7)
R2UR'UR2 (5,7)
27 27 UR2U2R (4,6)
U'R2U2R' (4,6)
28 28 R'U'RU'R (5,5)
RU'RU2R' (5,6)
RU2RU'R' (5,6)
29 29 U'R2U'R' (4,5)
F2R2U'F' (4,6)
U2R2UR (4,6)
30 30

R'FU'R' (4,4)
R2F'U'RF (5,6)
U'RU'R2U'R2 (6,8)
U'R2U'RU'R2 (6,8)

31 31 URU2R (4,5)
U'R'U'R2 (4,5)
32 32 U2RUR (4,5)
33 33 RU'RUR' (5,5)
RU2F'UF (5,6)
34 34

UR2U'F2R (5,7)
F'UR2U'R (5,6)
F2UF2R' (4,6)
R2U'F2R (4,6)
R2F2U'F2R (5,8)

35 35

FRUF'R2 (5,6)
R'FUFR' (5,5)
R'UFUR' (5,5)
R2FR2UR2 (5,8)
R2FR2U'R2 (5,8)
R2F'R2UR2 (5,8)
R2F'R2U'R2 (5,8)

36 36

FRFR' (4,4)
FR'U2F'U (5,6)
UFRU' (4,4)
R'UR2F'U2 (5,7)
R'F'URU (5,5)
R'U'R2F'U2 (5,7)

37 37

R'U'RFU' (5,5)
RU2FR'U' (5,6)
R'U2F'RU (5,6)

38 38

U2FRU' (4,5)
FR2FU'F' (5,6)
R'F'UR2F (5,6)

39 39

F'UR'F2U (5,6)
F'R'U2RU' (5,6)
R'U'FRU' (5,5)

40 40

U2R'F'U (4,5)

41 41

FU'RF2R' (5,6)
FU2RF'U' (5,6)
UR'F'R2U (5,6)
RU2FR'U' (5,6)
U'F'UR2F (5,6)
R'UFU2F' (5,6)

42 42

FUR'F'U (5,5)
UR'U'FU2 (5,6)
UR'U'F'U2 (5,6)
RU'FR2U' (5,6)
F2RU'FU' (5,6)

43 43

F'U'RU (4,4)
U'RUF'U' (5,5)
R2U'R2U'F' (5,7)

44 44

RUFU' (4,4)
RU'R2F'U (5,6)
F'URF'R (5,5)
U'F'R2UR (5,6)
U2RFRU' (5,6)

45 45

R2U'R2F' (4,6)

46 46

F'URU (4,4)
F'RFR (4,4)
UR2F'U2 (4,6)
U'R2FU2 (4,6)
U'R2F'U2 (4,6)

47 47

FRU2FU (5,6)
R'F2URF (5,6)
R2U'R2U2F' (5,8)

48 48

FR'U2RU' (5,6)

49 49

URFR2U' (5,6)
UR'FR2U' (5,6)
F'U'RF'R (5,5)
U'R'UR2F' (5,6)

50 50

FRU'R (4,4)
F'RF'R (4,4)