Skeletal Graph

The skeletal graph defines the topology. Each of the two continuous spaces formed by the surface can be retracted to the respective skeletal graph while maintaining the symmetry of the system. Grobe-Brauckmann has a good method for constructing the graph in "Gyroids of Constant Mean Curvature", 1997.

1. The system is defined by a rectangular box (dHx2dWx2dL). The box is divided into 4 equal boxes.
2. A first set of 4 points (V+) is located at {(3/4,3/4,1/4)d, (5/4,1/4,1/4)d, (3/4,5/4,3/4)d, (5/4,7/4,3/4)d}.
3. A second set of points (V-) is located at {(1/4,1/4,3/4)d, (7/4,3/4,3/4)d, (1/4,7/4,1/4)d, (7/4,5/4,1/4)d}.
4. Each set of points is connected by straight line segments.
5. Another series of lines are drawn in face diagonal directions at a length of d*(sqRt 2)/4.
6. The entire complex is copied down by distance of d and mirrored about its center.