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This post was crafted by Robert Yau and Kirjava in Google Docs.

17:25:19 < Robert> I just finished discovering that...

17:26:09 < Robert> 48/57 OLLs can be done using (sune variant), (U, U' , U2 or no move), (sune variant)

17:31:24 <+Kirjava> that's good

17:31:32 <+Kirjava> it means you can easily do the OLLCP subset where CP is already done

17:31:37 <+DanCohen> Holy **** sub-55 on 5x5x5 and on video!

Turns out, you can solve every case with Sune variations and some extra moves for alignment.

A lot of these algorithms are useful for OH. You may find that some of them are even better than your normal 2H OLL algorithms for OH!

Because of the notation used to describe these algorithms, there are cancellations that are undocumented. However, I doubt many of you will have trouble cancelling two sunes.

For each case, only one solution is documented - better ones may exist. Feel free to post them.

The notation describing the particular variation of Sune being used is as follows;

R = Right

L = Left

F = Front

B = Back

W = Wide

A = Anti

S = Sune

For example, RFS would be a regular Sune (RUR’URU2R’) while RBWAS would be the Right Back Wide AntiSune (r’U2RUR’Ur).

All edges flipped correctly

27 - (RFS)

26 - (RFAS)

21 - (RFAS)*2

22 - (RFS) U’ (RFS)

23 - (RBS) (RFS)

24 - (RFAS) U (RFS)

25 - (RFS) U (RBS)

No edges flipped correctly

1 - (RFWS) U’ (RBWAS)

2 - (RWS) U (RWS)

3 - (RWAS) U (RBWS)

4 - (RBWAS) U’ (RFWS)

20 - (RFWAS) M (RFS) U M’

17 - (RFWS) (LBWAS)

18 - (RFWS) (RBWS)

19 - (RBWAS) (RFWAS)

“P” shapes

31 - (RFAS) U (RFWS)

32 - (RBAS) U’ (RBWS)

43 - (RBWS) U’ (RBWAS)

44 - (RFWS) U (RFWAS)

“W” shapes

36 - (RFWS) U (RBWS)

37 - (RFWAS) U2 (RFS)

“L” shapes

47 - (RBWS) U (RBS)

48 - (RFWS) U’ (RFS)

53 - (RBWAS)*2

54 - (RFWAS)*2

49 - (RBS) (RFWAS)

50 - (RFS) (RBWAS)

“C” shapes

34 - (RBS) M’ (LBS) U M

46 - (RFS) M’ (RBS) U’ M

“T” shapes

33 - (RBS) (LBWS)

45 - (RFS) (RBWS)

“I” shapes

55 - (RFAS) U’ (RBWS)

56 - (RFAS) U’ M’ (RBS) U’ M

51 - (RFS) U’ (RFWS)

52 - (RFAS) U’ (RFWAS)

Square shapes

5 - (RBWAS)

6 - (RFWAS)

Big lightning

39 - (RFAS) (LBWS)

40 - (RBAS) (LFWS)

Small lightning

7 - (RFWS)

8 - (RBWS)

11 - M (RFS) U M’

12 - M’ (RBS) U’ M

Fish shapes

9 - M (RFAS) U’ M’

10 - M’ (RBAS) U M

35 - (RFAS)*2 (RBWAS)

37 - (RFWS) U (RBS)

Knight shapes

13 - (RBS)*2 (LBWAS)

14 - (RFS)*2 (LFWAS)

15 - (RBS) U’ (RFWAS)

16 - (RFS) U (RBWAS)

Awkward shapes

29 - (RFWS) U’ (RFAS)

30 - (RFS) U’ (RFWAS)

41 - (RFWAS) U’ (RFS)

42 - (RBWAS) U (RBS)

All corners oriented

28 - (RFWS) (RFAS)

57 - (RFAS) (RFWS)

17:25:19 < Robert> I just finished discovering that...

17:26:09 < Robert> 48/57 OLLs can be done using (sune variant), (U, U' , U2 or no move), (sune variant)

17:31:24 <+Kirjava> that's good

17:31:32 <+Kirjava> it means you can easily do the OLLCP subset where CP is already done

17:31:37 <+DanCohen> Holy **** sub-55 on 5x5x5 and on video!

Turns out, you can solve every case with Sune variations and some extra moves for alignment.

A lot of these algorithms are useful for OH. You may find that some of them are even better than your normal 2H OLL algorithms for OH!

Because of the notation used to describe these algorithms, there are cancellations that are undocumented. However, I doubt many of you will have trouble cancelling two sunes.

For each case, only one solution is documented - better ones may exist. Feel free to post them.

The notation describing the particular variation of Sune being used is as follows;

R = Right

L = Left

F = Front

B = Back

W = Wide

A = Anti

S = Sune

For example, RFS would be a regular Sune (RUR’URU2R’) while RBWAS would be the Right Back Wide AntiSune (r’U2RUR’Ur).

All edges flipped correctly

27 - (RFS)

26 - (RFAS)

21 - (RFAS)*2

22 - (RFS) U’ (RFS)

23 - (RBS) (RFS)

24 - (RFAS) U (RFS)

25 - (RFS) U (RBS)

No edges flipped correctly

1 - (RFWS) U’ (RBWAS)

2 - (RWS) U (RWS)

3 - (RWAS) U (RBWS)

4 - (RBWAS) U’ (RFWS)

20 - (RFWAS) M (RFS) U M’

17 - (RFWS) (LBWAS)

18 - (RFWS) (RBWS)

19 - (RBWAS) (RFWAS)

“P” shapes

31 - (RFAS) U (RFWS)

32 - (RBAS) U’ (RBWS)

43 - (RBWS) U’ (RBWAS)

44 - (RFWS) U (RFWAS)

“W” shapes

36 - (RFWS) U (RBWS)

37 - (RFWAS) U2 (RFS)

“L” shapes

47 - (RBWS) U (RBS)

48 - (RFWS) U’ (RFS)

53 - (RBWAS)*2

54 - (RFWAS)*2

49 - (RBS) (RFWAS)

50 - (RFS) (RBWAS)

“C” shapes

34 - (RBS) M’ (LBS) U M

46 - (RFS) M’ (RBS) U’ M

“T” shapes

33 - (RBS) (LBWS)

45 - (RFS) (RBWS)

“I” shapes

55 - (RFAS) U’ (RBWS)

56 - (RFAS) U’ M’ (RBS) U’ M

51 - (RFS) U’ (RFWS)

52 - (RFAS) U’ (RFWAS)

Square shapes

5 - (RBWAS)

6 - (RFWAS)

Big lightning

39 - (RFAS) (LBWS)

40 - (RBAS) (LFWS)

Small lightning

7 - (RFWS)

8 - (RBWS)

11 - M (RFS) U M’

12 - M’ (RBS) U’ M

Fish shapes

9 - M (RFAS) U’ M’

10 - M’ (RBAS) U M

35 - (RFAS)*2 (RBWAS)

37 - (RFWS) U (RBS)

Knight shapes

13 - (RBS)*2 (LBWAS)

14 - (RFS)*2 (LFWAS)

15 - (RBS) U’ (RFWAS)

16 - (RFS) U (RBWAS)

Awkward shapes

29 - (RFWS) U’ (RFAS)

30 - (RFS) U’ (RFWAS)

41 - (RFWAS) U’ (RFS)

42 - (RBWAS) U (RBS)

All corners oriented

28 - (RFWS) (RFAS)

57 - (RFAS) (RFWS)

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