"triangle rubik"-cube movements as list permutations.

tricube.py

moves = """
1	14	76
2	15	77
3	16	78
4	17	74
5	18	75
6	19	71
7	20	72
8	21	73
9	22	69
10	23	70
68	24	66
12	25	67
13	26	68
29	27	16
15	28	21
16	29	26
31	30	18
18	31	23
28	32	15
33	33	20
21	34	25
30	35	17
35	36	22
27	37	14
32	38	19
37	39	24
55	40	53
60	41	54
65	42	55
57	43	56
62	44	57
54	45	58
59	46	59
34	47	60
56	48	61
36	49	62
53	50	63
38	51	64
39	52	65
11	1	50
41	2	45
42	3	40
43	4	48
44	5	43
45	6	51
46	7	46
47	8	41
48	9	49
49	10	44
50	11	52
51	12	47
52	13	42
26	55	13
25	60	12
24	65	11
23	57	10
22	62	9
58	54	8
20	59	7
19	64	6
61	56	5
17	61	4
63	53	3
64	58	2
14	63	1
66	68	29
67	73	28
40	78	27
69	70	31
70	75	30
71	67	34
72	72	33
73	77	32
74	69	36
75	74	35
76	66	39
77	71	38
78	76	37
"""
	
moves = [[int(y) for y in x.split()] for x in moves.strip().split('\n')]		

def transpose(x):
    rows = len(x)
    cols = len(x[0])
    return [ [x[r][c] for r in range(rows)] for c in range(cols)]

[A, B, C] = transpose (moves)



def do(pos,move):
    return [move[pos[i]-1] for i in range(len(pos))]

I = range(1,79)

assert(do(do(do(I,A),A),A)==I)
assert(do(do(do(do(I,B),B),B),B)==I))
assert(do(do(do(do(I,C),C),C),C)==I)

def mm(pos,*moves):
    for m in moves:
        pos = do(pos, m)
    return pos

# FWD == B == roll forward
FWD = B
# C == rotate clockwise (w.r.t top layer)
CLCK = C
# BWD == roll backward
BWD = mm(I,FWD,FWD,FWD)
# CCLCK = rotate counter-clockwise
CCLCK = mm(I,CLCK,CLCK,CLCK)
# LEFT == roll to the left
LEFT = mm(I,CLCK,BWD,CCLCK)
# RIGHT == roll to the right
RIGHT = mm(I,CLCK,FWD,CCLCK)


assert(mm(I,A,A,A)==I)
assert(mm(I,FWD,FWD,FWD,FWD)==I)
assert(mm(I,CLCK,CLCK,CLCK,CLCK)==I)

assert(mm(I,CCLCK,CCLCK,CCLCK,CCLCK)==I)
assert(mm(I,BWD,BWD,BWD,BWD)==I)

assert(mm(I,LEFT,LEFT,LEFT)==RIGHT)

# rotate corners of top layer
# so that top surface moves towards player i.e. end up on front side
#      4-3
#      | |   top layer corners seen from above
#      1-2

R1 = A
R2 = mm(I,CLCK, R1, R1, CCLCK)
R3 = mm(I,CLCK, R2, CCLCK)
R4 = mm(I,CCLCK, R1, CLCK)

R2x = mm(I,LEFT,R1,R1,RIGHT)
R3x = mm(I, FWD, R2, BWD)
R4x = mm(I, FWD, R1, BWD)

assert (R2 == R2x)
assert (R3 == R3x)
assert (R4 == R4x)

# rotate corners of bottom layer
# so that bottom surface moves towards player, i.e. end up on front side
#      8-7
#      | |   bottom layer corners seen from above "through" the cube
#      5-6

R5 = mm(I,BWD, R1, R1, FWD)
R6 = mm(I,BWD, R2, R2, FWD)
R7 = mm(I,BWD, R6, FWD)
R8 = mm(I,BWD, R5, FWD)


def period(m):
    n = 1 
    x = I
    x = mm(x,m)
    while x != I:
        n += 1
        x = mm(x,m)
    return n    

X = mm(I,R1,R2,R3,R4)

X = mm(I,R1,R2,R2,R3,R3,R4)
		
print period(X)