Planes, channels and slices

The vertices of the honeycomb form an FCC (face-centred cubic) lattice. The whole construction is inscribed in a cube, and the 14 octahedra sit at the 8 corners + 6 face centres of that cube — this is the FCC motif.

In such a periodic lattice the nodes line up in straight through-rows only along a few low-index directions. Hence the three main families of planes:

• {111} — 4 orientations · triangular (close-packed) net · perpendicular to the cube diagonals <111>
• {100} — 3 orientations · square net · parallel to the cube faces <100>
• {110} — 6 orientations · rectangular net · perpendicular to the face diagonals <110>

In total — 13 orientations. Lines inside each plane run along <110> — the same “trunk channels” you see when looking through the cloud of nodes.

Press {111} / {100} / {110} — the camera turns perpendicular to the family, rotation stops, and the 3D cloud of nodes collapses into a flat net. Drag sideways with the mouse to see the same family as a stack of parallel planes.