156 N. Rivier and J.-F. Sadoc
Fig. 8.7.The overlap structure 3^2. 4. 3 .4. The main grid is that of the unit cell (a
square with a slight rhombohedral distortion). The secondary grid is made of the
mirror planesmandm′, bisecting the triangles. It has a rectangular unit cell with
half the area. There are two other strong alignments, on the directions (2,−1) and
(− 1 ,2) of the main grid, that include one diagonal of one of the two squares and
the intersection between two mirror lines bisecting the larger triangles. The aligned
points are equidistant. The transformation from one alignment to the other is a
rotation of 27 ◦=(3/2)(π/10). The overlap structure has many symmetries (unlike
the gap), responsible for the periodic, twist grain boundary stacking of sections of
intertwined collagen molecules that constitute the fibril of collagen
Fig. 8.8.The twist grain boundary between two overlap structures at successive
heights, rotated by 27 ◦. Note the periodic coincidence site lattice between equidis-
tant, aligned points