Changing z Value in Mathematica: Ideas?

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The discussion focuses on modifying the z-value in Mathematica's Table function to achieve specific output formats. A user seeks to change the z-value dynamically based on the x-value, proposing a solution with the expression Table[{x, -1, 1-x}. The conversation then shifts to creating a 3D graphic representation using Graphics3D, where users discuss simplifying the text annotations within the graphic. The final contributions include suggestions for combining and optimizing the code for generating a wurtzite structure, emphasizing a collaborative effort to refine the Mathematica code. Overall, the thread highlights practical coding techniques in Mathematica for visualizing mathematical structures.
B.Sam
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it could be stupid question for you...

if I input

Table[{x,-1,z},{x,0,6,1}]

I can get {{0,-1,z},{1,-1,z},{2,-1,z},{3,-1,z},{4,-1,z},{5,-1,z},{6,-1,z}}

is it possible to change the z value only...

what I want to get is like

{{0,-1,1},{1,-1,0},{2,-1,-1},{3,-1,-2},{4,-1,-3},{5,-1,-4},{6,-1,-5}}

as long as it shows the results like this with simple expression, it will be helpfull

have any idea?
 
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It looks like you want z to be equal to 1 - x.
So how about

Table[{x,-1,1-x},{x,0,6,1}]

?
 
that is easy!
great help

In addition,

I would like to get a resutls
like this
Graphics3D[{{RGBColor[1, 0, 0, .5],
Sphere[#, 0.2] & /@
Select[Table[{x, -1, 3 - x}, {x, -1, 3}],
Mod[Total[#], 2] == 0 &]}, Text[{-1, -1, 4}, {-1, -1, 4}],
Text[{0, -1, 3}, {0, -1, 3}], Text[{1, -1, 2}, {1, -1, 2}],
Text[{2, -1, 1}, {2, -1, 1}], Text[{3, -1, 0}, {3, -1, 0}]}]

is there anyway to simplify the Text part!

getting there!

even there are many things to ask...

I would like to sort it out myself first!

thank you very much
 
How about putting it in the table as well?
Code: 
Graphics3D[{
  {{RGBColor[1, 0, 0, .5], Sphere[#, 0.2]}, Text[#, #]} & /@ 
   Select[Table[{x, -1, 3 - x}, {x, -1, 3}], Mod[Total[#], 2] == 0 &]
  }]
 
it is easy!
fantastic!
basically, I have tried to make wurtzite structure by using mathematica.
I think that I have done it.
here is the code which I have done (this the best results in my ability)
is there any way to simplify this results


Graphics3D[{

(* the first layer of Ga atom *)

{RGBColor[1, 0, 0, .5],
Sphere[#, 0.2] & /@
Select[Table[{x, -1, 1 - x}, {x, -1, 3, 1}],
Mod[Total[#], 2] == 0 &]},
{RGBColor[1, 0, 0, .5],
Sphere[#, 0.2] & /@
Select[Table[{x, 0, 0 - x}, {x, -1, 3, 1}],
Mod[Total[#], 2] == 0 &]},
{RGBColor[1, 0, 0, .5],
Sphere[#, 0.2] & /@
Select[Table[{x, 1, -1 - x}, {x, -1, 3, 1}],
Mod[Total[#], 2] == 0 &]},
{RGBColor[1, 0, 0, .5],
Sphere[#, 0.2] & /@
Select[Table[{x, 2, -2 - x}, {x, -1, 3, 1}],
Mod[Total[#], 2] == 0 &]},
{RGBColor[1, 0, 0, .5],
Sphere[#, 0.2] & /@
Select[Table[{x, 3, -3 - x}, {x, -1, 3, 1}],
Mod[Total[#], 2] == 0 &]},

(* the second layer of Ga atom in [0001] direction *)

{RGBColor[1, 0, 0, .5],
Sphere[#, 0.2] & /@
Select[Table[{x, 0, 2 - x}, {x, -1, 3, 1}],
Mod[Total[#], 2] == 0 &]},
{RGBColor[1, 0, 0, .5],
Sphere[#, 0.2] & /@
Select[Table[{x, 1, 1 - x}, {x, -1, 3, 1}],
Mod[Total[#], 2] == 0 &]},
{RGBColor[1, 0, 0, .5],
Sphere[#, 0.2] & /@
Select[Table[{x, 2, 0 - x}, {x, -1, 3, 1}],
Mod[Total[#], 2] == 0 &]},
{RGBColor[1, 0, 0, .5],
Sphere[#, 0.2] & /@
Select[Table[{x, 3, -1 - x}, {x, -1, 3, 1}],
Mod[Total[#], 2] == 0 &]},
{RGBColor[1, 0, 0, .5],
Sphere[#, 0.2] & /@
Select[Table[{x, 4, -2 - x}, {x, -1, 3, 1}],
Mod[Total[#], 2] == 0 &]},

(* the third layer of Ga atom in [0001] direction *)

{RGBColor[1, 0, 0, .5],
Sphere[#, 0.2] & /@
Select[Table[{x + 4/3, -1 + 4/3, 1 - x + 4/3}, {x, -1, 3, 1}],
Mod[Total[#], 2] == 0 &]},
{RGBColor[1, 0, 0, .5],
Sphere[#, 0.2] & /@
Select[Table[{x + 4/3, 0 + 4/3, 0 - x + 4/3}, {x, -1, 3, 1}],
Mod[Total[#], 2] == 0 &]},
{RGBColor[1, 0, 0, .5],
Sphere[#, 0.2] & /@
Select[Table[{x + 4/3, 1 + 4/3, -1 - x + 4/3}, {x, -1, 3, 1}],
Mod[Total[#], 2] == 0 &]},
{RGBColor[1, 0, 0, .5],
Sphere[#, 0.2] & /@
Select[Table[{x + 4/3, 2 + 4/3, -2 - x + 4/3}, {x, -1, 3, 1}],
Mod[Total[#], 2] == 0 &]},
{RGBColor[1, 0, 0, .5],
Sphere[#, 0.2] & /@
Select[Table[{x + 4/3, 3 + 4/3, -3 - x + 4/3}, {x, -1, 3, 1}],
Mod[Total[#], 2] == 0 &]},

(* the fourth layer of Ga atom in [0001] direction *)

{RGBColor[1, 0, 0, .5],
Sphere[#, 0.2] & /@
Select[Table[{x + 4/3, 0 + 4/3, 2 - x + 4/3}, {x, -1, 3, 1}],
Mod[Total[#], 2] == 0 &]},
{RGBColor[1, 0, 0, .5],
Sphere[#, 0.2] & /@
Select[Table[{x + 4/3, 1 + 4/3, 1 - x + 4/3}, {x, -1, 3, 1}],
Mod[Total[#], 2] == 0 &]},
{RGBColor[1, 0, 0, .5],
Sphere[#, 0.2] & /@
Select[Table[{x + 4/3, 2 + 4/3, 0 - x + 4/3}, {x, -1, 3, 1}],
Mod[Total[#], 2] == 0 &]},
{RGBColor[1, 0, 0, .5],
Sphere[#, 0.2] & /@
Select[Table[{x + 4/3, 3 + 4/3, -1 - x + 4/3}, {x, -1, 3, 1}],
Mod[Total[#], 2] == 0 &]},
{RGBColor[1, 0, 0, .5],
Sphere[#, 0.2] & /@
Select[Table[{x + 4/3, 4 + 4/3, -2 - x + 4/3}, {x, -1, 3, 1}],
Mod[Total[#], 2] == 0 &]},

(* the fifth layer of Ga atom in [0001] direction *)

{RGBColor[1, 0, 0, .5],
Sphere[#, 0.2] & /@
Select[Table[{(x + 4/3) + 4/3, (-1 + 4/3) + 4/3, (1 - x + 4/3) +
4/3}, {x, -1, 3, 1}], Mod[Total[#], 2] == 0 &]},
{RGBColor[1, 0, 0, .5],
Sphere[#, 0.2] & /@
Select[Table[{(x + 4/3) + 4/3, (0 + 4/3) + 4/3, (0 - x + 4/3) + 4/
3}, {x, -1, 3, 1}], Mod[Total[#], 2] == 0 &]},
{RGBColor[1, 0, 0, .5],
Sphere[#, 0.2] & /@
Select[Table[{(x + 4/3) + 4/3, (1 + 4/3) + 4/3, (-1 - x + 4/3) +
4/3}, {x, -1, 3, 1}], Mod[Total[#], 2] == 0 &]},
{RGBColor[1, 0, 0, .5],
Sphere[#, 0.2] & /@
Select[Table[{(x + 4/3) + 4/3, (2 + 4/3) + 4/3, (-2 - x + 4/3) +
4/3}, {x, -1, 3, 1}], Mod[Total[#], 2] == 0 &]},
{RGBColor[1, 0, 0, .5],
Sphere[#, 0.2] & /@
Select[Table[{(x + 4/3) + 4/3, (3 + 4/3) + 4/3, (-3 - x + 4/3) +
4/3}, {x, -1, 3, 1}], Mod[Total[#], 2] == 0 &]},

(* the first layer of N atom *)

{RGBColor[1, 5, 4, .5],
Sphere[#, 0.1] & /@
Select[Table[{x + 1/2, -1 + 1/2, 1 - x + 1/2}, {x, -1, 3, 1}],
Mod[Total[#], 2] == 1.5 &]},
{RGBColor[1, 5, 4, .5],
Sphere[#, 0.1] & /@
Select[Table[{x + 1/2, 0 + 1/2, 0 - x + 1/2}, {x, -1, 3, 1}],
Mod[Total[#], 2] == 1.5 &]},
{RGBColor[1, 5, 4, .5],
Sphere[#, 0.1] & /@
Select[Table[{x + 1/2, 1 + 1/2, -1 - x + 1/2}, {x, -1, 3, 1}],
Mod[Total[#], 2] == 1.5 &]},
{RGBColor[1, 5, 4, .5],
Sphere[#, 0.1] & /@
Select[Table[{x + 1/2, 2 + 1/2, -2 - x + 1/2}, {x, -1, 3, 1}],
Mod[Total[#], 2] == 1.5 &]},
{RGBColor[1, 5, 4, .5],
Sphere[#, 0.1] & /@
Select[Table[{x + 1/2, 3 + 1/2, -3 - x + 1/2}, {x, -1, 3, 1}],
Mod[Total[#], 2] == 1.5 &]},

(* the second layer of N atom *)

{RGBColor[1, 5, 4, .5],
Sphere[#, 0.1] & /@
Select[Table[{x + 1/2, 0 + 1/2, 2 - x + 1/2}, {x, -1, 3, 1}],
Mod[Total[#], 2] == 1.5 &]},
{RGBColor[1, 5, 4, .5],
Sphere[#, 0.1] & /@
Select[Table[{x + 1/2, 1 + 1/2, 1 - x + 1/2}, {x, -1, 3, 1}],
Mod[Total[#], 2] == 1.5 &]},
{RGBColor[1, 5, 4, .5],
Sphere[#, 0.1] & /@
Select[Table[{x + 1/2, 2 + 1/2, 0 - x + 1/2}, {x, -1, 3, 1}],
Mod[Total[#], 2] == 1.5 &]},
{RGBColor[1, 5, 4, .5],
Sphere[#, 0.1] & /@
Select[Table[{x + 1/2, 3 + 1/2, -1 - x + 1/2}, {x, -1, 3, 1}],
Mod[Total[#], 2] == 1.5 &]},
{RGBColor[1, 5, 4, .5],
Sphere[#, 0.1] & /@
Select[Table[{x + 1/2, 4 + 1/2, -2 - x + 1/2}, {x, -1, 3, 1}],
Mod[Total[#], 2] == 1.5 &]},

(* the third layer of N atom *)

{RGBColor[1, 5, 4, .5],
Sphere[#, 0.1] & /@
Select[Table[{(x + 4/3) + 1/2, (-1 + 4/3) + 1/2, (1 - x + 4/3) +
1/2}, {x, -1, 3, 1}], Mod[Total[#], 2] == 1.5 &]},
{RGBColor[1, 5, 4, .5],
Sphere[#, 0.1] & /@
Select[Table[{(x + 4/3) + 1/2, (0 + 4/3) + 1/2, (0 - x + 4/3) + 1/
2}, {x, -1, 3, 1}], Mod[Total[#], 2] == 1.5 &]},
{RGBColor[1, 5, 4, .5],
Sphere[#, 0.1] & /@
Select[Table[{(x + 4/3) + 1/2, (1 + 4/3) + 1/2, (-1 - x + 4/3) +
1/2}, {x, -1, 3, 1}], Mod[Total[#], 2] == 1.5 &]},
{RGBColor[1, 5, 4, .5],
Sphere[#, 0.1] & /@
Select[Table[{(x + 4/3) + 1/2, (2 + 4/3) + 1/2, (-2 - x + 4/3) +
1/2}, {x, -1, 3, 1}], Mod[Total[#], 2] == 1.5 &]},
{RGBColor[1, 5, 4, .5],
Sphere[#, 0.1] & /@
Select[Table[{(x + 4/3) + 1/2, (3 + 4/3) + 1/2, (-3 - x + 4/3) +
1/2}, {x, -1, 3, 1}], Mod[Total[#], 2] == 1.5 &]},

(* the fourth layer of N atom *)

{RGBColor[1, 5, 4, .5],
Sphere[#, 0.1] & /@
Select[Table[{(x + 4/3) + 1/2, (0 + 4/3) + 1/2, (2 - x + 4/3) + 1/
2}, {x, -1, 3, 1}], Mod[Total[#], 2] == 1.5 &]},
{RGBColor[1, 5, 4, .5],
Sphere[#, 0.1] & /@
Select[Table[{(x + 4/3) + 1/2, (1 + 4/3) + 1/2, (1 - x + 4/3) + 1/
2}, {x, -1, 3, 1}], Mod[Total[#], 2] == 1.5 &]},
{RGBColor[1, 5, 4, .5],
Sphere[#, 0.1] & /@
Select[
Table[{(x + 4/3) + 1/2, (2 + 4/3) + 1/2, (0 - x + 4/3) + 1/
2}, {x, -1, 3, 1}], Mod[Total[#], 2] == 1.5 &]},
{RGBColor[1, 5, 4, .5],
Sphere[#, 0.1] & /@
Select[Table[{(x + 4/3) + 1/2, (3 + 4/3) + 1/2, (-1 - x + 4/3) +
1/2}, {x, -1, 3, 1}], Mod[Total[#], 2] == 1.5 &]},
{RGBColor[1, 5, 4, .5],
Sphere[#, 0.1] & /@
Select[Table[{(x + 4/3) + 1/2, (4 + 4/3) + 1/2, (-2 - x + 4/3) +
1/2}, {x, -1, 3, 1}], Mod[Total[#], 2] == 1.5 &]},

(* the fifth layer of N atom *)

{RGBColor[1, 5, 4, .5],
Sphere[#, 0.1] & /@
Select[Table[{((x + 4/3) + 4/3) + 1/2, ((-1 + 4/3) + 4/3) + 1/
2, ((1 - x + 4/3) + 4/3) + 1/2}, {x, -1, 3, 1}],
Mod[Total[#], 2] == 1.5 &]},
{RGBColor[1, 5, 4, .5],
Sphere[#, 0.1] & /@
Select[Table[{((x + 4/3) + 4/3) + 1/2, ((0 + 4/3) + 4/3) + 1/
2, ((0 - x + 4/3) + 4/3) + 1/2}, {x, -1, 3, 1}],
Mod[Total[#], 2] == 1.5 &]},
{RGBColor[1, 5, 4, .5],
Sphere[#, 0.1] & /@
Select[
Table[{((x + 4/3) + 4/3) + 1/2, ((1 + 4/3) + 4/3) + 1/
2, ((-1 - x + 4/3) + 4/3) + 1/2}, {x, -1, 3, 1}],
Mod[Total[#], 2] == 1.5 &]},
{RGBColor[1, 5, 4, .5],
Sphere[#, 0.1] & /@
Select[Table[{((x + 4/3) + 4/3) + 1/2, ((2 + 4/3) + 4/3) + 1/
2, ((-2 - x + 4/3) + 4/3) + 1/2}, {x, -1, 3, 1}],
Mod[Total[#], 2] == 1.5 &]},
{RGBColor[1, 5, 4, .5],
Sphere[#, 0.1] & /@
Select[Table[{((x + 4/3) + 4/3) + 1/2, ((3 + 4/3) + 4/3) + 1/
2, ((-3 - x + 4/3) + 4/3) + 1/2}, {x, -1, 3, 1}],
Mod[Total[#], 2] == 1.5 &]},
 
that was too long
so here is rest part of it
just combine together!

Thick,

(*bonding between the first Ga atom layer and the first N atom in [
0001] direction*)

{RGBColor[0, 1, 0],
Line[Table[{{x, -1, 1 - x}, {x + 1/2, -1 + 1/2,
1 - x + 1/2}}, {x, -1, 3, 1}]]},

{RGBColor[0, 1, 0],
Line[Table[{{x, 0, 0 - x}, {x + 1/2, 0 + 1/2,
0 - x + 1/2}}, {x, -1, 3, 1}]]},

{RGBColor[0, 1, 0],
Line[Table[{{x, 1, -1 - x}, {x + 1/2,
1 + 1/2, -1 - x + 1/2}}, {x, -1, 3, 1}]]},

{RGBColor[0, 1, 0],
Line[Table[{{x, 2, -2 - x}, {x + 1/2,
2 + 1/2, -2 - x + 1/2}}, {x, -1, 3, 1}]]},

{RGBColor[0, 1, 0],
Line[Table[{{x, 3, -3 - x}, {x + 1/2,
3 + 1/2, -3 - x + 1/2}}, {x, -1, 3, 1}]]},

(*bonding between the first Ga atom layer and the first N atom in [
0001] direction*)

{RGBColor[0, 1, 0],
Line[Table[{{x, 0, 2 - x}, {x + 1/2, -1 + 1/2,
1 - x + 1/2}}, {x, -1, 3, 1}]]},
{RGBColor[0, 1, 0],
Line[Table[{{x, 0, 2 - x}, {(x + 1/2) - 1, (-1 + 1/2) + 1,
1 - x + 1/2}}, {x, 0, 3, 1}]]},
{RGBColor[0, 1, 0],
Line[Table[{{x, 0,
2 - x}, {(x + 1/2) - 1, -1 + 1/2, (1 - x + 1/2) + 1}}, {x, 0,
3, 1}]]},

{RGBColor[0, 1, 0],
Line[Table[{{x, 1, 1 - x}, {x + 1/2, 0 + 1/2,
0 - x + 1/2}}, {x, -1, 3, 1}]]},
{RGBColor[0, 1, 0],
Line[Table[{{x, 1, 1 - x}, {(x + 1/2) - 1, (0 + 1/2) + 1,
0 - x + 1/2}}, {x, 0, 3, 1}]]},
{RGBColor[0, 1, 0],
Line[Table[{{x, 1, 1 - x}, {(x + 1/2) - 1,
0 + 1/2, (0 - x + 1/2) + 1}}, {x, 0, 3, 1}]]},

{RGBColor[0, 1, 0],
Line[Table[{{x, 2, 0 - x}, {x + 1/2,
1 + 1/2, -1 - x + 1/2}}, {x, -1, 3, 1}]]},
{RGBColor[0, 1, 0],
Line[Table[{{x, 2,
0 - x}, {(x + 1/2) - 1, (1 + 1/2) + 1, -1 - x + 1/2}}, {x, 0,
3, 1}]]},
{RGBColor[0, 1, 0],
Line[Table[{{x, 2, 0 - x}, {(x + 1/2) - 1,
1 + 1/2, (-1 - x + 1/2) + 1}}, {x, 0, 3, 1}]]},

{RGBColor[0, 1, 0],
Line[Table[{{x, 3, -1 - x}, {x + 1/2,
2 + 1/2, -2 - x + 1/2}}, {x, -1, 3, 1}]]},
{RGBColor[0, 1, 0],
Line[Table[{{x,
3, -1 - x}, {(x + 1/2) - 1, (2 + 1/2) + 1, -2 - x + 1/2}}, {x,
0, 3, 1}]]},
{RGBColor[0, 1, 0],
Line[Table[{{x, 3, -1 - x}, {(x + 1/2) - 1,
2 + 1/2, (-2 - x + 1/2) + 1}}, {x, 0, 3, 1}]]},

{RGBColor[0, 1, 0],
Line[Table[{{x, 4, -2 - x}, {x + 1/2,
3 + 1/2, -3 - x + 1/2}}, {x, -1, 3, 1}]]},
{RGBColor[0, 1, 0],
Line[Table[{{x, 4, -2 - x}, {(x + 1/2) - 1,
3 + 1/2, (-3 - x + 1/2) + 1}}, {x, 0, 3, 1}]]},

(*bonding between the second Ga atom layer and the second N atom in \
[0001] direction*)

{RGBColor[0, 1, 0],
Line[Table[{{x, 0, 2 - x}, {x + 1/2, 0 + 1/2,
2 - x + 1/2}}, {x, -1, 3, 1}]]},

{RGBColor[0, 1, 0],
Line[Table[{{x, 1, 1 - x}, {x + 1/2, 1 + 1/2,
1 - x + 1/2}}, {x, -1, 3, 1}]]},

{RGBColor[0, 1, 0],
Line[Table[{{x, 2, 0 - x}, {x + 1/2, 2 + 1/2,
0 - x + 1/2}}, {x, -1, 3, 1}]]},

{RGBColor[0, 1, 0],
Line[Table[{{x, 3, -1 - x}, {x + 1/2,
3 + 1/2, -1 - x + 1/2}}, {x, -1, 3, 1}]]},

{RGBColor[0, 1, 0],
Line[Table[{{x, 4, -2 - x}, {x + 1/2,
4 + 1/2, -2 - x + 1/2}}, {x, -1, 3, 1}]]},

(*bonding between the second N atom layer and the third Ga atom \
layer in [0001] direction*)

{RGBColor[0, 1, 0],
Line[Table[{{x + 1/2, 0 + 1/2, 2 - x + 1/2}, {x + 4/3, -1 + 4/3,
1 - x + 4/3}}, {x, -1, 3, 1}]]},
{RGBColor[0, 1, 0],
Line[Table[{{x + 1/2, 0 + 1/2,
2 - x + 1/2}, {x + 4/3 - 1, (-1 + 4/3) +
1, (1 - x + 4/3)}}, {x, 0, 3, 1}]]},
{RGBColor[0, 1, 0],
Line[Table[{{x + 1/2, 0 + 1/2,
2 - x + 1/2}, {x + 4/3 - 1, -1 + 4/3, (1 - x + 4/3) + 1}}, {x,
0, 3, 1}]]},

{RGBColor[0, 1, 0],
Line[Table[{{x + 1/2, 1 + 1/2, 1 - x + 1/2}, {x + 4/3, 0 + 4/3,
0 - x + 4/3}}, {x, -1, 3, 1}]]},
{RGBColor[0, 1, 0],
Line[Table[{{x + 1/2, 1 + 1/2,
1 - x + 1/2}, {x + 4/3 - 1, (0 + 4/3) + 1, (0 - x + 4/3)}}, {x,
0, 3, 1}]]},
{RGBColor[0, 1, 0],
Line[Table[{{x + 1/2, 1 + 1/2, 1 - x + 1/2}, {x + 4/3 - 1,
0 + 4/3, (0 - x + 4/3) + 1}}, {x, 0, 3, 1}]]},

{RGBColor[0, 1, 0],
Line[Table[{{x + 1/2, 2 + 1/2, 0 - x + 1/2}, {x + 4/3,
1 + 4/3, -1 - x + 4/3}}, {x, -1, 3, 1}]]},
{RGBColor[0, 1, 0],
Line[Table[{{x + 1/2, 2 + 1/2,
0 - x + 1/2}, {x + 4/3 - 1, (1 + 4/3) +
1, (-1 - x + 4/3)}}, {x, 0, 3, 1}]]},
{RGBColor[0, 1, 0],
Line[Table[{{x + 1/2, 2 + 1/2, 0 - x + 1/2}, {x + 4/3 - 1,
1 + 4/3, (-1 - x + 4/3) + 1}}, {x, 0, 3, 1}]]},

{RGBColor[0, 1, 0],
Line[Table[{{x + 1/2, 3 + 1/2, -1 - x + 1/2}, {x + 4/3,
2 + 4/3, -2 - x + 4/3}}, {x, -1, 3, 1}]]},
{RGBColor[0, 1, 0],
Line[Table[{{x + 1/2,
3 + 1/2, -1 - x + 1/2}, {x + 4/3 - 1, (2 + 4/3) +
1, (-2 - x + 4/3)}}, {x, 0, 3, 1}]]},
{RGBColor[0, 1, 0],
Line[Table[{{x + 1/2, 3 + 1/2, -1 - x + 1/2}, {x + 4/3 - 1,
2 + 4/3, (-2 - x + 4/3) + 1}}, {x, 0, 3, 1}]]},

{RGBColor[0, 1, 0],
Line[Table[{{x + 1/2, 4 + 1/2, -2 - x + 1/2}, {x + 4/3,
3 + 4/3, -3 - x + 4/3}}, {x, -1, 3, 1}]]},
{RGBColor[0, 1, 0],
Line[Table[{{x + 1/2, 4 + 1/2, -2 - x + 1/2}, {x + 4/3 - 1,
3 + 4/3, (-3 - x + 4/3) + 1}}, {x, 0, 3, 1}]]},

(*bonding between the third Ga atom layer and the third N atom \
layer in [0001] direction*)

{RGBColor[0, 1, 0],
Line[Table[{{x + 4/3, -1 + 4/3,
1 - x + 4/3}, {(x + 4/3) + 1/2, (-1 + 4/3) + 1/
2, (1 - x + 4/3) + 1/2}}, {x, -1, 3, 1}]]},

{RGBColor[0, 1, 0],
Line[Table[{{x + 4/3, 0 + 4/3,
0 - x + 4/3}, {(x + 4/3) + 1/2, (0 + 4/3) + 1/
2, (0 - x + 4/3) + 1/2}}, {x, -1, 3, 1}]]},

{RGBColor[0, 1, 0],
Line[Table[{{x + 4/3,
1 + 4/3, -1 - x + 4/3}, {(x + 4/3) + 1/2, (1 + 4/3) + 1/
2, (-1 - x + 4/3) + 1/2}}, {x, -1, 3, 1}]]},

{RGBColor[0, 1, 0],
Line[Table[{{x + 4/3,
2 + 4/3, -2 - x + 4/3}, {(x + 4/3) + 1/2, (2 + 4/3) + 1/
2, (-2 - x + 4/3) + 1/2}}, {x, -1, 3, 1}]]},

{RGBColor[0, 1, 0],
Line[Table[{{x + 4/3,
3 + 4/3, -3 - x + 4/3}, {(x + 4/3) + 1/2, (3 + 4/3) + 1/
2, (-3 - x + 4/3) + 1/2}}, {x, -1, 3, 1}]]},

(*bonding between the fourth Ga atom layer and the third N atom \
layer in [0001] direction*)

{RGBColor[0, 1, 0],
Line[Table[{{x + 4/3, 0 + 4/3,
2 - x + 4/3}, {(x + 4/3) + 1/2, (-1 + 4/3) + 1/
2, (1 - x + 4/3) + 1/2}}, {x, -1, 3, 1}]]},
{RGBColor[0, 1, 0],
Line[Table[{{x + 4/3, 0 + 4/3,
2 - x + 4/3}, {((x + 4/3) + 1/2) - 1, ((-1 + 4/3) + 1/2) +
1, (1 - x + 4/3) + 1/2}}, {x, 0, 3, 1}]]},
{RGBColor[0, 1, 0],
Line[Table[{{x + 4/3, 0 + 4/3,
2 - x + 4/3}, {((x + 4/3) + 1/2) - 1, (-1 + 4/3) + 1/
2, ((1 - x + 4/3) + 1/2) + 1}}, {x, 0, 3, 1}]]},

{RGBColor[0, 1, 0],
Line[Table[{{x + 4/3, 1 + 4/3,
1 - x + 4/3}, {(x + 4/3) + 1/2, (0 + 4/3) + 1/
2, (0 - x + 4/3) + 1/2}}, {x, -1, 3, 1}]]},
{RGBColor[0, 1, 0],
Line[Table[{{x + 4/3, 1 + 4/3,
1 - x + 4/3}, {((x + 4/3) + 1/2) - 1, ((0 + 4/3) + 1/2) +
1, (0 - x + 4/3) + 1/2}}, {x, 0, 3, 1}]]},
{RGBColor[0, 1, 0],
Line[Table[{{x + 4/3, 1 + 4/3,
1 - x + 4/3}, {((x + 4/3) + 1/2) - 1, (0 + 4/3) + 1/
2, ((0 - x + 4/3) + 1/2) + 1}}, {x, 0, 3, 1}]]},

{RGBColor[0, 1, 0],
Line[Table[{{x + 4/3, 2 + 4/3,
0 - x + 4/3}, {(x + 4/3) + 1/2, (1 + 4/3) + 1/
2, (-1 - x + 4/3) + 1/2}}, {x, -1, 3, 1}]]},
{RGBColor[0, 1, 0],
Line[Table[{{x + 4/3, 2 + 4/3,
0 - x + 4/3}, {((x + 4/3) + 1/2) - 1, ((1 + 4/3) + 1/2) +
1, (-1 - x + 4/3) + 1/2}}, {x, 0, 3, 1}]]},
{RGBColor[0, 1, 0],
Line[Table[{{x + 4/3, 2 + 4/3,
0 - x + 4/3}, {((x + 4/3) + 1/2) - 1, (1 + 4/3) + 1/
2, ((-1 - x + 4/3) + 1/2) + 1}}, {x, 0, 3, 1}]]},

{RGBColor[0, 1, 0],
Line[Table[{{x + 4/3,
3 + 4/3, -1 - x + 4/3}, {(x + 4/3) + 1/2, (2 + 4/3) + 1/
2, (-2 - x + 4/3) + 1/2}}, {x, -1, 3, 1}]]},
{RGBColor[0, 1, 0],
Line[Table[{{x + 4/3,
3 + 4/3, -1 - x + 4/3}, {((x + 4/3) + 1/2) -
1, ((2 + 4/3) + 1/2) + 1, (-2 - x + 4/3) + 1/2}}, {x, 0, 3,
1}]]},
{RGBColor[0, 1, 0],
Line[Table[{{x + 4/3,
3 + 4/3, -1 - x + 4/3}, {((x + 4/3) + 1/2) - 1, (2 + 4/3) + 1/
2, ((-2 - x + 4/3) + 1/2) + 1}}, {x, 0, 3, 1}]]},

{RGBColor[0, 1, 0],
Line[Table[{{x + 4/3,
4 + 4/3, -2 - x + 4/3}, {(x + 4/3) + 1/2, (3 + 4/3) + 1/
2, (-3 - x + 4/3) + 1/2}}, {x, -1, 3, 1}]]},
{RGBColor[0, 1, 0],
Line[Table[{{x + 4/3,
4 + 4/3, -2 - x + 4/3}, {((x + 4/3) + 1/2) - 1, (3 + 4/3) + 1/
2, ((-3 - x + 4/3) + 1/2) + 1}}, {x, 0, 3, 1}]]},

(*bonding between the fourth Ga atom layer and the fourth N atom in \
[0001] direction*)

{RGBColor[0, 1, 0],
Line[Table[{{x + 4/3, 0 + 4/3,
2 - x + 4/3}, {(x + 4/3) + 1/2, (0 + 4/3) + 1/
2, (2 - x + 4/3) + 1/2}}, {x, -1, 3, 1}]]},

{RGBColor[0, 1, 0],
Line[Table[{{x + 4/3, 1 + 4/3,
1 - x + 4/3}, {(x + 4/3) + 1/2, (1 + 4/3) + 1/
2, (1 - x + 4/3) + 1/2}}, {x, -1, 3, 1}]]},

{RGBColor[0, 1, 0],
Line[Table[{{x + 4/3, 2 + 4/3,
0 - x + 4/3}, {(x + 4/3) + 1/2, (2 + 4/3) + 1/
2, (0 - x + 4/3) + 1/2}}, {x, -1, 3, 1}]]},

{RGBColor[0, 1, 0],
Line[Table[{{x + 4/3,
3 + 4/3, -1 - x + 4/3}, {(x + 4/3) + 1/2, (3 + 4/3) + 1/
2, (-1 - x + 4/3) + 1/2}}, {x, -1, 3, 1}]]},

{RGBColor[0, 1, 0],
Line[Table[{{x + 4/3,
4 + 4/3, -2 - x + 4/3}, {(x + 4/3) + 1/2, (4 + 4/3) + 1/
2, (-2 - x + 4/3) + 1/2}}, {x, -1, 3, 1}]]},

(*bonding between the fourth N atom layer and the fifth Ga atom \
layer in [0001] direction*)

{RGBColor[0, 1, 0],
Line[Table[{{(x + 4/3) + 1/2, (0 + 4/3) + 1/2, (2 - x + 4/3) + 1/
2}, {(x + 4/3) + 4/3, (-1 + 4/3) + 4/3, (1 - x + 4/3) + 4/
3}}, {x, -1, 3, 1}]]},
{RGBColor[0, 1, 0],
Line[Table[{{(x + 4/3) + 1/2, (0 + 4/3) + 1/2, (2 - x + 4/3) + 1/
2}, {((x + 4/3) + 4/3) - 1, ((-1 + 4/3) + 4/3) +
1, (1 - x + 4/3) + 4/3}}, {x, 0, 3, 1}]]},
{RGBColor[0, 1, 0],
Line[Table[{{(x + 4/3) + 1/2, (0 + 4/3) + 1/2, (2 - x + 4/3) + 1/
2}, {((x + 4/3) + 4/3) - 1, (-1 + 4/3) + 4/
3, ((1 - x + 4/3) + 4/3) + 1}}, {x, 0, 3, 1}]]},

{RGBColor[0, 1, 0],
Line[Table[{{(x + 4/3) + 1/2, (1 + 4/3) + 1/2, (1 - x + 4/3) + 1/
2}, {(x + 4/3) + 4/3, (0 + 4/3) + 4/3, (0 - x + 4/3) + 4/
3}}, {x, -1, 3, 1}]]},
{RGBColor[0, 1, 0],
Line[Table[{{(x + 4/3) + 1/2, (1 + 4/3) + 1/2, (1 - x + 4/3) + 1/
2}, {((x + 4/3) + 4/3) - 1, ((0 + 4/3) + 4/3) +
1, (0 - x + 4/3) + 4/3}}, {x, 0, 3, 1}]]},
{RGBColor[0, 1, 0],
Line[Table[{{(x + 4/3) + 1/2, (1 + 4/3) + 1/2, (1 - x + 4/3) + 1/
2}, {((x + 4/3) + 4/3) - 1, (0 + 4/3) + 4/
3, ((0 - x + 4/3) + 4/3) + 1}}, {x, 0, 3, 1}]]},

{RGBColor[0, 1, 0],
Line[Table[{{(x + 4/3) + 1/2, (2 + 4/3) + 1/2, (0 - x + 4/3) + 1/
2}, {(x + 4/3) + 4/3, (1 + 4/3) + 4/3, (-1 - x + 4/3) + 4/
3}}, {x, -1, 3, 1}]]},
{RGBColor[0, 1, 0],
Line[Table[{{(x + 4/3) + 1/2, (2 + 4/3) + 1/2, (0 - x + 4/3) + 1/
2}, {((x + 4/3) + 4/3) - 1, ((1 + 4/3) + 4/3) +
1, (-1 - x + 4/3) + 4/3}}, {x, 0, 3, 1}]]},
{RGBColor[0, 1, 0],
Line[Table[{{(x + 4/3) + 1/2, (2 + 4/3) + 1/2, (0 - x + 4/3) + 1/
2}, {((x + 4/3) + 4/3) - 1, (1 + 4/3) + 4/
3, ((-1 - x + 4/3) + 4/3) + 1}}, {x, 0, 3, 1}]]},

{RGBColor[0, 1, 0],
Line[Table[{{(x + 4/3) + 1/2, (3 + 4/3) + 1/2, (-1 - x + 4/3) + 1/
2}, {(x + 4/3) + 4/3, (2 + 4/3) + 4/3, (-2 - x + 4/3) + 4/
3}}, {x, -1, 3, 1}]]},
{RGBColor[0, 1, 0],
Line[Table[{{(x + 4/3) + 1/2, (3 + 4/3) + 1/2, (-1 - x + 4/3) + 1/
2}, {((x + 4/3) + 4/3) - 1, ((2 + 4/3) + 4/3) +
1, (-2 - x + 4/3) + 4/3}}, {x, 0, 3, 1}]]},
{RGBColor[0, 1, 0],
Line[Table[{{(x + 4/3) + 1/2, (3 + 4/3) + 1/2, (-1 - x + 4/3) + 1/
2}, {((x + 4/3) + 4/3) - 1, (2 + 4/3) + 4/
3, ((-2 - x + 4/3) + 4/3) + 1}}, {x, 0, 3, 1}]]},

{RGBColor[0, 1, 0],
Line[Table[{{(x + 4/3) + 1/2, (4 + 4/3) + 1/2, (-2 - x + 4/3) + 1/
2}, {(x + 4/3) + 4/3, (3 + 4/3) + 4/3, (-3 - x + 4/3) + 4/
3}}, {x, -1, 3, 1}]]},
{RGBColor[0, 1, 0],
Line[Table[{{(x + 4/3) + 1/2, (4 + 4/3) + 1/2, (-2 - x + 4/3) + 1/
2}, {((x + 4/3) + 4/3) - 1, (3 + 4/3) + 4/
3, ((-3 - x + 4/3) + 4/3) + 1}}, {x, 0, 3, 1}]]},

(*bonding between the fifth Ga atom layer and the fifth N atom in [
0001] direction*)

{RGBColor[0, 1, 0],
Line[Table[{{(x + 4/3) + 4/3, (-1 + 4/3) + 4/3, (1 - x + 4/3) + 4/
3}, {((x + 4/3) + 4/3) + 1/2, ((-1 + 4/3) + 4/3) + 1/
2, ((1 - x + 4/3) + 4/3) + 1/2}}, {x, -1, 3, 1}]]},

{RGBColor[0, 1, 0],
Line[Table[{{(x + 4/3) + 4/3, (0 + 4/3) + 4/3, (0 - x + 4/3) + 4/
3}, {((x + 4/3) + 4/3) + 1/2, ((0 + 4/3) + 4/3) + 1/
2, ((0 - x + 4/3) + 4/3) + 1/2}}, {x, -1, 3, 1}]]},

{RGBColor[0, 1, 0],
Line[Table[{{(x + 4/3) + 4/3, (1 + 4/3) + 4/3, (-1 - x + 4/3) + 4/
3}, {((x + 4/3) + 4/3) + 1/2, ((1 + 4/3) + 4/3) + 1/
2, ((-1 - x + 4/3) + 4/3) + 1/2}}, {x, -1, 3, 1}]]},

{RGBColor[0, 1, 0],
Line[Table[{{(x + 4/3) + 4/3, (2 + 4/3) + 4/3, (-2 - x + 4/3) + 4/
3}, {((x + 4/3) + 4/3) + 1/2, ((2 + 4/3) + 4/3) + 1/
2, ((-2 - x + 4/3) + 4/3) + 1/2}}, {x, -1, 3, 1}]]},

{RGBColor[0, 1, 0],
Line[Table[{{(x + 4/3) + 4/3, (3 + 4/3) + 4/3, (-3 - x + 4/3) + 4/
3}, {((x + 4/3) + 4/3) + 1/2, ((3 + 4/3) + 4/3) + 1/
2, ((-3 - x + 4/3) + 4/3) + 1/2}}, {x, -1, 3, 1}]]}

}, ImageSize -> 600, Boxed -> False]
 

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