2003 December
 Xah
 xah@xahlee.org
 http://xahlee.org/PageTwo_dir/more.html

honeycomb grid with triangle overall shape

e

r = Sin[Pi/3]*2;
iMax = 9;

h = Sin[Pi/3]*r;
pts = 
        Table[Point@List[j*2*r/2 + r/2*(iMax - i), h*(iMax - i)], {i, 
            iMax, 0, -1}, {j, i, 0, -1}];

Graphics[pts, AspectRatio -> 1, Frame -> True] // 
      Show

hexagon = 
      Line@Table[{Cos@x, Sin@x}, {x, 0 + 2*Pi/6/2, 2*Pi + 2*Pi/6/2, 
            2*Pi/6}]

Graphics[hexagon, AspectRatio -> 1, Frame -> True] // 
      Show

gp = 
        pts /. {Point[coord_] :> 
              Map[(coord + #) &, hexagon, {2}]};

Graphics[gp, AspectRatio -> Automatic, Frame -> True] // 
      Show