Slicing a gyroid network with a rhombic dodecahedron allows you so see some of the interesting patterns and symmetries. Notice the different silhouettes when viewing along the 3-face vertex versus the 4-face vertex.

See video here: https://youtu.be/mj3Wa0exTqc

See here for a gyroid surface for remixing: https://www.thingiverse.com/thing:4794791