Sentence:  The lattice points that lie in this plane are the vertices of the regular tessellation {3, 4} of equilateral triangles, and the other points just mentioned are the vertices of the <WSD>quasiregular</WSD> tessellation <small>\begin{Bmatrix} 3 \\ 4 \end{Bmatrix}</small> of triangles and hexagons [9, p. 60]. 
Meaning of the word marked with <WSD> tags:  That is semiregular with regular faces of precisely two types that alternate around each vertex.