The two arrows in the schematic pictures indicate
the two sides about which the two stacked tiles are
allowed to hinge.
For example, the configuration I-1 (click on the I1-I3 image below) can be directly opened
to obtain the starting configuration
RRRURRRU or the ring shape
RRmRRmRRmRRm
or the ring shape
RRmRRmRRmRRm ,
whereas the configuration I-3 can be opened into
RmRvRmLvRmRvRmLv
,
whereas the configuration I-3 can be opened into
RmRvRmLvRmRvRmLv (and also into the starting 2x4 configuration).
(and also into the starting 2x4 configuration).
  
S1-S4:
  
S1-S4:   
L1-L8:
  
L1-L8:   
U1-U6:
  
U1-U6: 