+ # The explicit formula for this angle would be:
+ #
+ # pi + pi / 6 + (((self.index + 1) % 6) // 2) * pi * 2 / 3
+ #
+ # The meaning of the part regarding the index is the following:
+ # - rotate the indices by 1
+ # - group by 2 (because couples of triangles move together in the
+ # plan)
+ # - multiply the group by a rotation factor
+ #
+ # The explicit formula shows clearly that triangles move in groups of
+ # 2 in the plan.
+ #
+ # However, use an implicit form for robustness, so that if the other
+ # angle functions change this one can be left untouched.
+ return self.get_angle_in_hexagon() - self.get_angle_in_plan()
+
+ def get_angle_in_backface_relative_to_hexagon(self):
+
+ """"Get the angle of the triangle in the backface relative to the
+ rotation of the same triangle in the hexagon."""
+
+ backface_triangle_index = self.get_backface_index()
+ # group triangles in couples
+ group = (((backface_triangle_index + 1) % 6) // 2)
+ return pi + pi * 2 / 3 * group