$RU$ means rotate right face up. And so on.

Define operation $M=RD\cdot DR\cdot RU \cdot DR \cdot FC\cdot DL\cdot FA$

$U$ : Up
$D$:  Down
$L$: Left
$R$: Right
$F$: Front
$B$: Back
$C$: Clockwise
$A$: Anticlockwise

$C$

$R$

LA

means: the down left back block rotates clockwisely(look at the vortex),
              the down left front block moves to the right,
              the down right back block stays rest,
              the down right front block moves to left and then rotates anticlockwisely.

$M$ =

$M^2$=

$M^{-1}=$

$M^{-2}=$

$C$

$R$

LA

$A$

$A$

$A$

$A$

$RC$

$L$

$C$

$C$

$C$

NOTATION

A: (0, 0)
a: 1
B = Translate(A, (0, 2))
C = Translate(A, (2, 2))
D = Translate(A, (2, 0))
L = Translate(A, (0, 1))
R = Translate(A, (2, 1))
U = Translate(A, (1, 2))
M = Translate(A, (1, 0))
f = Segment(A, B)
g = Segment(B, C)
h = Segment(C, D)
i = Segment(D, A)
j = Segment(L, R)
k = Segment(U, M)
m = Translate({f, g, h, i, j, k}, (3, -3))
m2 = Translate({f, g, h, i, j, k}, (3, -7))
mi = Translate({f, g, h, i, j, k}, (8, -3))
mi2 = Translate({f, g, h, i, j, k}, (8, -7))
l = Segment((-1, -0.5), (15, -0.5))