Jelly, 3938 bytes
×ばつtṭ‘Ä©8ịðiị"\Œg’D¤ṃ"FRB"ṄȧƲị®œ×ばつtṭ‘Ä©8ịðiị(BgDŻ¤ṃ"FRB"ṄȧƲị®œ?8ðƒ®
×ばつtṭ‘Ä©8ịðiị"\Œg’D¤ṃ"FRB"ṄȧƲị®œ×ばつtṭ‘Ä©8ịðiị(BgDŻ¤ṃ"FRB"ṄȧƲị®œ?8ðƒ® - Link: list of integers, Faces×ばつtṭ‘ - code page indices -> [1,224,132,17,116,224]
Ä - cumulative sums -> [1,225,357,374,490,714]
= the permutation indices of:
[no-op, F, RF, RB, B, FF] from [1,2,3,4,5,6]
© - ...and copy that to the register
8ị - Faces indexed into {that} -> P
ð ðƒ® - starting with the register, reduce P by - f(Current, PValue):
i - 1-index of {PValue} in {Current}
Ʋ - last four links as a monad - SideEffect(X=that):
ị - 1-index {X} into:
¤ - nilad followed by links as a nilad
"\Œg’(Bg - 31760417604
D - to decimal -> [3[1,7,6,0,4]
Ż - prefix with a zero -> [0,1,7,6,0,4]
ṃ"FRB" - convert to base three with digits 120 as FRB
Ṅ - print {that} to stdout and yield {that}
ȧ - {that} logical AND {X} -> X
ị® - 1-index {X} into the register
œ?8 - permutation of {Current} at {that} index -> Next
Jelly, 39 bytes
×ばつtṭ‘Ä©8ịðiị"\Œg’D¤ṃ"FRB"ṄȧƲị®œ?8ðƒ®
×ばつtṭ‘Ä©8ịðiị"\Œg’D¤ṃ"FRB"ṄȧƲị®œ?8ðƒ® - Link: list of integers, Faces×ばつtṭ‘ - code page indices -> [1,224,132,17,116,224]
Ä - cumulative sums -> [1,225,357,374,490,714]
= the permutation indices of:
[no-op, F, RF, RB, B, FF] from [1,2,3,4,5,6]
© - ...and copy that to the register
8ị - Faces indexed into {that} -> P
ð ðƒ® - starting with the register, reduce P by - f(Current, PValue):
i - 1-index of {PValue} in {Current}
Ʋ - last four links as a monad - SideEffect(X=that):
ị - 1-index {X} into:
¤ - nilad followed by links as a nilad
"\Œg’ - 317604
D - to decimal -> [3,1,7,6,0,4]
ṃ"FRB" - convert to base three with digits 120 as FRB
Ṅ - print that to stdout ȧ - {that} logical AND {X} -> X
ị® - 1-index {X} into the register
œ?8 - permutation of {Current} at {that} index -> Next
Jelly, 38 bytes
×ばつtṭ‘Ä©8ịðiị(BgDŻ¤ṃ"FRB"ṄȧƲị®œ?8ðƒ®
×ばつtṭ‘Ä©8ịðiị(BgDŻ¤ṃ"FRB"ṄȧƲị®œ?8ðƒ® - Link: list of integers, Faces×ばつtṭ‘ - code page indices -> [1,224,132,17,116,224]
Ä - cumulative sums -> [1,225,357,374,490,714]
= the permutation indices of:
[no-op, F, RF, RB, B, FF] from [1,2,3,4,5,6]
© - ...and copy that to the register
8ị - Faces indexed into {that} -> P
ð ðƒ® - starting with the register, reduce P by - f(Current, PValue):
i - 1-index of {PValue} in {Current}
Ʋ - last four links as a monad - SideEffect(X=that):
ị - 1-index {X} into:
¤ - nilad followed by links as a nilad
(Bg - 17604
D - to decimal -> [1,7,6,0,4]
Ż - prefix with a zero -> [0,1,7,6,0,4]
ṃ"FRB" - convert to base three with digits 120 as FRB
Ṅ - print {that} to stdout and yield {that}
ȧ - {that} logical AND {X} -> X
ị® - 1-index {X} into the register
œ?8 - permutation of {Current} at {that} index -> Next
Jelly, 39 bytes
×ばつtṭ‘Ä©8ịðiị"\Œg’D¤ṃ"FRB"ṄȧƲị®œ?8ðƒ®
A monadic Link that accepts a list of face numbers (not starting with 1 and without any equal neighbours) and prints to stdout as a side effect (and yields a list of numbers, which may be ignored).
How?
Permute some permutation indices :)
×ばつtṭ‘Ä©8ịðiị"\Œg’D¤ṃ"FRB"ṄȧƲị®œ?8ðƒ® - Link: list of integers, Faces×ばつtṭ‘ - code page indices -> [1,224,132,17,116,224]
Ä - cumulative sums -> [1,225,357,374,490,714]
= the permutation indices of:
[no-op, F, RF, RB, B, FF] from [1,2,3,4,5,6]
© - ...and copy that to the register
8ị - Faces indexed into {that} -> P
ð ðƒ® - starting with the register, reduce P by - f(Current, PValue):
i - 1-index of {PValue} in {Current}
Ʋ - last four links as a monad - SideEffect(X=that):
ị - 1-index {X} into:
¤ - nilad followed by links as a nilad
"\Œg’ - 317604
D - to decimal -> [3,1,7,6,0,4]
ṃ"FRB" - convert to base three with digits 120 as FRB
Ṅ - print that to stdout
ȧ - {that} logical AND {X} -> X
ị® - 1-index {X} into the register
œ?8 - permutation of {Current} at {that} index -> Next