Changing z Value in Mathematica: Ideas?

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Discussion Overview

The discussion revolves around generating specific output in Mathematica using the Table function, particularly focusing on modifying the z value in a 3D graphics context. Participants explore various methods to achieve desired outputs, including graphical representations and simplifications of code.

Discussion Character

  • Exploratory
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant asks how to change the z value in a Table output to achieve a specific format.
  • Another participant suggests setting z to be equal to 1 - x as a solution.
  • A participant expresses satisfaction with the solution and seeks further simplification for a Graphics3D command involving text elements.
  • Another participant proposes integrating text into the table structure for simplification.
  • A participant shares their attempt to create a wurtzite structure in Mathematica and requests ways to simplify their complex code.

Areas of Agreement / Disagreement

Participants generally agree on the methods proposed for modifying the z value and simplifying the code, but there is no consensus on the best approach for the graphical representation or further simplifications.

Contextual Notes

The discussion includes various assumptions about the capabilities of Mathematica and the specific requirements for graphical outputs, which may not be fully addressed in the provided solutions.

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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