Crystallographic terminology associated with the honeycomb structure
the concept of lattice is very (too!) often misinterpreted outside crystallography. By definition, the lattice points are all identical, that is each lattice point has identical surroundings to all others. In a honeycomb pattern you can distinguish 2 different sets of points, the red and the blue ones in the figure.
So honeycomb pattern is actually a 2-dimensional structure (not a lattice), resulting from the convolution of a basis (in this casis constituted of one blu + one red point) with a 2D lattice (the hexagonal one in the figure representing the five nets)