Hexagonal Pattern Made of Tetrahedra

Take a tetrahedron with each face colored differently. Place six such tetrahedra on a flat surface around an open hexagon. Unfold three faces of each tetrahedron into the flat surface to produce a hexagon of triangles. Place such patterns side by side to cover the flat surface. If you were to roll a colored tetrahedron on that flat pattern, then the face color of the tetrahedron touching the pattern would always match the color of the pattern.