ClearAll[triHex];
triHex[w_, h_] := Module[{hex = {FaceForm[White], EdgeForm[Black], Polygon@#,
Red, PointSize[Large], Point@#} &@ Table[{Cos[2 Pi k /6], Sin[2 Pi
kPolygon /6]},@ {k#, 6}]}Red,
Fold[Translate[#,Point {{0,@ 0#}, ## & @@@ #2CirclePoints[6]}] &, hex
Translate[hex,
Join @@ {Table[{42 kj Cos[Pi/3]+ i, 0i Sqrt[3]}, {k, 1i, w }]0, Table[2 kh {Cos[Pi/3],- Sin[Pi/3]1}, {kj, 10, hw }]- 1}]]]]]
Examples:
Graphics[triHex[10, 5], ImageSize -> 600]
Graphics[triHex[7, 7] /. White -> LightBlue, ImageSize -> 600]