v = {1, 0};
w = {-1/2, Sqrt[3]/2};
a = Arrow[{{0, 0}, v}];
b = Arrow[{{0, 0}, w}];
g = Polygon[{2 v + w, v + 2 w, w - v, -2 v - w, -v - 2 w, v - w}/3];
d1 = {{Line[{2 v + w, -2 v - w}/3],
    Line[{2 v + w, -2 v - w}/6 + {w, w}/2]}, {Dashed,
    Line[{2 v + w, -2 v - w}/6 5/3 + {w, w}/6],
    Line[{2 v + w, -2 v - w}/6 4/3 - {w, w}/3]}, {Dotted,
    Line[{2 v + w, -2 v - w}/6 4/3 + {w, w}/3],
    Line[{2 v + w, -2 v - w}/6 5/3 - {w, w}/6]}};
c = {Line[{-v/2, v/2}], Line[{-w/2, w/2}]};

gr1 = Graphics[{{LightGray, g}, {Purple, a}, {Blue, b}, {Lighter[Red],
      Thickness[.015], c}, {Thickness[.005], d1}}];
Show[gr1]

v = {1, 0};
w = {-1/2, Sqrt[3]/2};
a = Arrow[{{0, 0}, v}];
b = Arrow[{{0, 0}, w}];
g = Polygon[{{0, 0}, v, v + w, w}];
d1 = {{Line[{{0, 0}, 2 v + w}/2],
    Line[{{0, 0}, 2 v + w}/2 + {w, w}/2]},
   {Dashed, Line[{{0, 0}, 2 v + w}/2 + {w, w}/6],
    Line[{{0, 0}, 2 v + w}/3 + 2 {w, w}/3],
    Line[{4 v + 2 w, 6 v + 3 w}/6 - {w, w}/3]}, {Dotted,
    Line[{{0, 0}, 2 v + w}/2 + {w, w}/3],
    Line[{{0, 0}, 2 v + w}/6 + 5 {w, w}/6],
    Line[{2 v + w, 6 v + 3 w}/6 - {w, w}/6]}};
c = {Line[{3 v, 4 v + 2 w, 4 w + 2 v, 3 w}/6],
   Line[{6 v + 3 w, 4 v + 2 w}/6], Line[{4 w + 2 v, 6 w + 3 v}/6]};

gr2 = Graphics[{{LightGray, g}, {Purple, a}, {Blue, b}, {Lighter[Red],
      Thickness[.015], c}, {Thickness[.005], d1}}];
Show[gr2]

Show[gr1, Translate[#, {Sqrt[3], 0}] & /@ gr2, ImageSize -> 500]

***

v = {1, 0};
w = {-1/2, Sqrt[3]/2};
a = Arrow[{{0, 0}, v}];
b = Arrow[{{0, 0}, w}];
g = Polygon[{2 v + w, v + 2 w, w - v, -2 v - w, -v - 2 w, v - w}/3];
d1 = {Line[{(-7 v - 5 w)/12, (7 v + 5 w)/12}],
   Line[{(-7 v - 5 w)/12, (7 v + 5 w)/18} - {w - v, w - v}/6],
   Line[{(-7 v - 5 w)/36, (7 v + 5 w)/12} + {w - v, w - v}/4],
   Line[{(-7 v - 5 w)/12, (7 v + 5 w)/12} + {w - v, w - v}/12],
   Line[{(-7 v - 5 w)/12, (7 v + 5 w)/12} - {w - v, w - v}/12],
   Line[{(-7 v - 5 w)/12, (7 v + 5 w)/36} - {w - v, w - v}/4],
   Line[{(-7 v - 5 w)/18, (7 v + 5 w)/12} + {w - v, w - v}/6]};
c = {Line[{-v/2, v/2}], Line[{-w/2, w/2}]};

gr1 = Graphics[{{LightGray, g}, {Purple, a}, {Blue, b}, {Lighter[Red],
      Thickness[.015], c}, {Thickness[.005], d1}}];
Show[gr1]

v = {1, 0};
w = {-1/2, Sqrt[3]/2};
a = Arrow[{{0, 0}, v}];
b = Arrow[{{0, 0}, w}];
g = Polygon[{{0, 0}, v, v + w, w}];
d1 = {Line[{{0, 0}, 7 v + 5 w}/7],
   Line[{{0, 0}, 7 v + 5 w} 2/35 + {w, w} 5/7],
   Line[{{0, 0}, 7 v + 5 w} 3/35 + {v, v} 2/5],
   Line[{{0, 0}, 7 v + 5 w} 4/35 + {w, w} 3/7],
   Line[{{0, 0}, 7 v + 5 w} 1/35 + {v, v} 4/5],
   Line[{{0, 0}, 7 v + 5 w} 1/7 + {w, w} 1/7],
   Line[{{0, 0}, 7 v + 5 w} 1/35 + {w, w} 6/7],
   Line[{{0, 0}, 7 v + 5 w} 4/35 + {v, v} 1/5],
   Line[{{0, 0}, 7 v + 5 w} 3/35 + {w, w} 4/7],
   Line[{{0, 0}, 7 v + 5 w} 2/35 + {v, v} 3/5],
   Line[{{0, 0}, 7 v + 5 w} 5/35 + {w, w} 2/7]};
c = {Line[{3 v, 4 v + 2 w, 4 w + 2 v, 3 w}/6],
   Line[{6 v + 3 w, 4 v + 2 w}/6], Line[{4 w + 2 v, 6 w + 3 v}/6]};

gr2 = Graphics[{{LightGray, g}, {Purple, a}, {Blue, b}, {Lighter[Red],
      Thickness[.015], c}, {Thickness[.005], d1}}];
Show[gr2]

Show[gr1, Translate[#, {Sqrt[3], 0}] & /@ gr2, ImageSize -> 500]