Pooling3D.nb

(* Content-type: application/vnd.wolfram.mathematica *)

(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)

(* CreatedBy='Mathematica 12.1' *)

(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[       158,          7]
NotebookDataLength[     37879,        874]
NotebookOptionsPosition[     36295,        842]
NotebookOutlinePosition[     36692,        858]
CellTagsIndexPosition[     36649,        855]
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{
Cell[BoxData[
 RowBox[{"FactorInteger", "[", "96", "]"}]], "Input",
 CellLabel->"In[53]:=",ExpressionUUID->"18bb20ad-2eca-4536-820b-83197ca20997"],

Cell[BoxData[
 RowBox[{"8", "*", "4", "*", "3"}]], "Input",
 CellLabel->"In[54]:=",ExpressionUUID->"56b70a0d-2237-4ef0-8b07-9874ffdc09ee"],

Cell[BoxData[{
 RowBox[{
  RowBox[{"pts", " ", "=", " ", 
   RowBox[{"Flatten", "@", 
    RowBox[{"Table", "[", 
     RowBox[{
      RowBox[{"Point", "[", 
       RowBox[{"{", 
        RowBox[{"x", ",", " ", "y", ",", " ", "z"}], "}"}], "]"}], ",", " ", 
      RowBox[{"{", 
       RowBox[{"x", ",", " ", "1", ",", " ", "8"}], "}"}], ",", " ", 
      RowBox[{"{", 
       RowBox[{"y", ",", " ", "1", ",", " ", "4"}], "}"}], ",", " ", 
      RowBox[{"{", 
       RowBox[{"z", ",", " ", "1", ",", " ", "3"}], "}"}]}], "]"}]}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"pos", "=", 
   RowBox[{"RandomChoice", "[", 
    RowBox[{"pts", ",", " ", "3"}], "]"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"neg", " ", "=", " ", 
   RowBox[{"Complement", "[", 
    RowBox[{"pts", ",", " ", "pos"}], "]"}]}], ";"}]}], "Input",
 CellLabel->"In[55]:=",ExpressionUUID->"e8f277a8-95c5-4a68-8b8c-e621b0ab63a3"],

Cell[BoxData[
 RowBox[{"dots", "=", 
  RowBox[{"Graphics3D", "[", 
   RowBox[{
    RowBox[{"{", 
     RowBox[{
      RowBox[{"PointSize", "[", "Large", "]"}], ",", " ", "Red", ",", " ", 
      "pos", ",", " ", "Black", ",", " ", "neg"}], "}"}], ",", " ", 
    RowBox[{"Axes", "\[Rule]", "True"}], ",", " ", 
    RowBox[{"Ticks", "\[Rule]", 
     RowBox[{"{", 
      RowBox[{
       RowBox[{"Range", "[", 
        RowBox[{"1", ",", "8"}], "]"}], ",", " ", 
       RowBox[{"Range", "[", 
        RowBox[{"1", ",", "4"}], "]"}], ",", " ", 
       RowBox[{"Range", "[", 
        RowBox[{"1", ",", "3"}], "]"}]}], "}"}]}]}], "]"}]}]], "Input",
 CellLabel->"In[58]:=",ExpressionUUID->"4b199021-aa3f-498f-bafc-ffa1babeae44"],

Cell["Pool by each dimension. First coordinate:", "Text",ExpressionUUID->"2d851b6b-9e09-4f49-b69b-41a3f3e99bb1"],

Cell[BoxData[{
 RowBox[{
  RowBox[{"xcoords", "=", 
   RowBox[{"Select", "[", 
    RowBox[{
     RowBox[{"Range", "[", 
      RowBox[{"1", ",", " ", "8"}], "]"}], ",", " ", 
     RowBox[{
      RowBox[{
       RowBox[{"Cases", "[", 
        RowBox[{"pos", ",", " ", 
         RowBox[{"Point", "[", 
          RowBox[{"{", 
           RowBox[{"#", ",", " ", "_", ",", " ", "_"}], "}"}], "]"}]}], "]"}],
        "!=", 
       RowBox[{"{", "}"}]}], "&"}]}], "]"}]}], ";"}], "\n", 
 RowBox[{
  RowBox[{"xplanes", " ", "=", " ", 
   RowBox[{
    RowBox[{
     RowBox[{"ParametricPlot3D", "[", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{"#", ",", " ", "u", ",", " ", "v"}], "}"}], ",", " ", 
       RowBox[{"{", 
        RowBox[{"u", ",", " ", "1", ",", " ", "4"}], "}"}], ",", " ", 
       RowBox[{"{", 
        RowBox[{"v", ",", " ", "1", ",", " ", "3"}], "}"}], ",", 
       RowBox[{"PlotStyle", "\[Rule]", 
        RowBox[{"{", 
         RowBox[{"Purple", ",", " ", 
          RowBox[{"Opacity", "[", "0.25", "]"}]}], "}"}]}], ",", " ", 
       RowBox[{"Mesh", "->", "None"}]}], "]"}], "&"}], "/@", "xcoords"}]}], 
  ";"}], "\n", 
 RowBox[{
  RowBox[{"ycoords", "=", 
   RowBox[{"Select", "[", 
    RowBox[{
     RowBox[{"Range", "[", 
      RowBox[{"1", ",", " ", "4"}], "]"}], ",", " ", 
     RowBox[{
      RowBox[{
       RowBox[{"Cases", "[", 
        RowBox[{"pos", ",", " ", 
         RowBox[{"Point", "[", 
          RowBox[{"{", 
           RowBox[{"_", ",", " ", "#", ",", " ", "_"}], "}"}], "]"}]}], "]"}],
        "!=", 
       RowBox[{"{", "}"}]}], "&"}]}], "]"}]}], ";"}], "\n", 
 RowBox[{
  RowBox[{"yplanes", "=", 
   RowBox[{
    RowBox[{
     RowBox[{"ParametricPlot3D", "[", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{"u", ",", "#", ",", " ", "v"}], "}"}], ",", " ", 
       RowBox[{"{", 
        RowBox[{"u", ",", " ", "1", ",", " ", "8"}], "}"}], ",", " ", 
       RowBox[{"{", 
        RowBox[{"v", ",", " ", "1", ",", " ", "3"}], "}"}], ",", 
       RowBox[{"PlotStyle", "\[Rule]", 
        RowBox[{"{", 
         RowBox[{"Blue", ",", " ", 
          RowBox[{"Opacity", "[", "0.25", "]"}]}], "}"}]}], ",", " ", 
       RowBox[{"Mesh", "->", "None"}]}], "]"}], "&"}], "/@", "ycoords"}]}], 
  ";"}], "\n", 
 RowBox[{
  RowBox[{"zcoords", "=", 
   RowBox[{"Select", "[", 
    RowBox[{
     RowBox[{"Range", "[", 
      RowBox[{"1", ",", " ", "3"}], "]"}], ",", " ", 
     RowBox[{
      RowBox[{
       RowBox[{"Cases", "[", 
        RowBox[{"pos", ",", " ", 
         RowBox[{"Point", "[", 
          RowBox[{"{", 
           RowBox[{"_", ",", " ", "_", ",", " ", "#"}], "}"}], "]"}]}], "]"}],
        "!=", 
       RowBox[{"{", "}"}]}], "&"}]}], "]"}]}], ";"}], "\n", 
 RowBox[{
  RowBox[{"zplanes", " ", "=", " ", 
   RowBox[{
    RowBox[{
     RowBox[{"ParametricPlot3D", "[", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{"u", ",", "v", ",", " ", "#"}], "}"}], ",", " ", 
       RowBox[{"{", 
        RowBox[{"u", ",", " ", "1", ",", " ", "8"}], "}"}], ",", " ", 
       RowBox[{"{", 
        RowBox[{"v", ",", " ", "1", ",", " ", "4"}], "}"}], ",", 
       RowBox[{"PlotStyle", "\[Rule]", 
        RowBox[{"{", 
         RowBox[{"Green", ",", " ", 
          RowBox[{"Opacity", "[", "0.25", "]"}]}], "}"}]}], ",", " ", 
       RowBox[{"Mesh", "->", "None"}]}], "]"}], "&"}], "/@", "zcoords"}]}], 
  ";"}]}], "Input",ExpressionUUID->"54b2a133-23e2-482a-b05a-d2e5a07d5c26"],

Cell[BoxData[
 RowBox[{"Show", "[", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{
    "zplanes", ",", " ", "xplanes", ",", " ", "yplanes", ",", " ", "dots"}], 
    "}"}], ",", " ", 
   RowBox[{"PlotRange", "\[Rule]", "Full"}], ",", 
   RowBox[{"Ticks", "\[Rule]", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"Range", "[", 
       RowBox[{"1", ",", "8"}], "]"}], ",", " ", 
      RowBox[{"Range", "[", 
       RowBox[{"1", ",", "4"}], "]"}], ",", " ", 
      RowBox[{"Range", "[", 
       RowBox[{"1", ",", "3"}], "]"}]}], "}"}]}]}], "]"}]], "Input",
 CellLabel->"In[65]:=",ExpressionUUID->"cbe629c7-ccf9-4804-8c5b-383339583d90"],

Cell[CellGroupData[{

Cell["2x2 Example", "Subsubsection",ExpressionUUID->"60b6e213-e296-4c53-88b4-78a4a54c747e"],

Cell[BoxData[{
 RowBox[{
  RowBox[{"pts", " ", "=", " ", 
   RowBox[{"Flatten", "@", 
    RowBox[{"Table", "[", 
     RowBox[{
      RowBox[{"Point", "[", 
       RowBox[{"{", 
        RowBox[{"x", ",", " ", "y", ",", " ", "z"}], "}"}], "]"}], ",", " ", 
      RowBox[{"{", 
       RowBox[{"x", ",", " ", "1", ",", " ", "2"}], "}"}], ",", " ", 
      RowBox[{"{", 
       RowBox[{"y", ",", " ", "1", ",", " ", "2"}], "}"}], ",", " ", 
      RowBox[{"{", 
       RowBox[{"z", ",", " ", "1", ",", " ", "2"}], "}"}]}], "]"}]}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"pos", "=", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"Point", "[", 
      RowBox[{"{", 
       RowBox[{"1", ",", "1", ",", " ", "1"}], "}"}], "]"}], ",", " ", 
     RowBox[{"Point", "[", 
      RowBox[{"{", 
       RowBox[{"2", ",", " ", "2", ",", " ", "2"}], "}"}], "]"}]}], "}"}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"neg", " ", "=", " ", 
   RowBox[{"Complement", "[", 
    RowBox[{"pts", ",", " ", "pos"}], "]"}]}], ";"}]}], "Input",
 CellLabel->"In[1]:=",ExpressionUUID->"7867bf1b-b945-4f6f-b14d-eb8f8d30d6ba"],

Cell[CellGroupData[{

Cell[BoxData["pts"], "Input",
 CellLabel->"In[4]:=",ExpressionUUID->"9d2a2d95-4543-441d-8393-e55318779207"],

Cell[BoxData[
 RowBox[{"{", 
  RowBox[{
   RowBox[{"Point", "[", 
    RowBox[{"{", 
     RowBox[{"1", ",", "1", ",", "1"}], "}"}], "]"}], ",", 
   RowBox[{"Point", "[", 
    RowBox[{"{", 
     RowBox[{"1", ",", "1", ",", "2"}], "}"}], "]"}], ",", 
   RowBox[{"Point", "[", 
    RowBox[{"{", 
     RowBox[{"1", ",", "2", ",", "1"}], "}"}], "]"}], ",", 
   RowBox[{"Point", "[", 
    RowBox[{"{", 
     RowBox[{"1", ",", "2", ",", "2"}], "}"}], "]"}], ",", 
   RowBox[{"Point", "[", 
    RowBox[{"{", 
     RowBox[{"2", ",", "1", ",", "1"}], "}"}], "]"}], ",", 
   RowBox[{"Point", "[", 
    RowBox[{"{", 
     RowBox[{"2", ",", "1", ",", "2"}], "}"}], "]"}], ",", 
   RowBox[{"Point", "[", 
    RowBox[{"{", 
     RowBox[{"2", ",", "2", ",", "1"}], "}"}], "]"}], ",", 
   RowBox[{"Point", "[", 
    RowBox[{"{", 
     RowBox[{"2", ",", "2", ",", "2"}], "}"}], "]"}]}], "}"}]], "Output",
 CellLabel->"Out[4]=",ExpressionUUID->"2ff3130b-83d0-40c9-8366-a2f84b40778f"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"dots", "=", 
   RowBox[{"Graphics3D", "[", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{
       RowBox[{"PointSize", "[", "0.06", "]"}], ",", " ", "Red", ",", " ", 
       "pos", ",", " ", 
       RowBox[{"Lighter", "[", "Blue", "]"}], ",", " ", 
       RowBox[{"{", 
        RowBox[{
         RowBox[{"Point", "[", 
          RowBox[{"{", 
           RowBox[{"1", ",", "1", ",", "2"}], "}"}], "]"}], ",", 
         RowBox[{"Point", "[", 
          RowBox[{"{", 
           RowBox[{"1", ",", "2", ",", "1"}], "}"}], "]"}], ",", 
         RowBox[{"Point", "[", 
          RowBox[{"{", 
           RowBox[{"1", ",", "2", ",", "2"}], "}"}], "]"}]}], "}"}], ",", 
       "  ", "Black", ",", " ", 
       RowBox[{"{", 
        RowBox[{
         RowBox[{"Point", "[", 
          RowBox[{"{", 
           RowBox[{"2", ",", "1", ",", "1"}], "}"}], "]"}], ",", 
         RowBox[{"Point", "[", 
          RowBox[{"{", 
           RowBox[{"2", ",", "1", ",", "2"}], "}"}], "]"}], ",", 
         RowBox[{"Point", "[", 
          RowBox[{"{", 
           RowBox[{"2", ",", "2", ",", "1"}], "}"}], "]"}]}], "}"}]}], "}"}], 
     ",", " ", 
     RowBox[{"Axes", "\[Rule]", "True"}], ",", " ", 
     RowBox[{"Ticks", "\[Rule]", "None"}]}], "]"}]}], ";"}], "\n", 
 RowBox[{
  RowBox[{"extra", " ", "=", " ", "0.25"}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"xcoords", "=", 
   RowBox[{"Select", "[", 
    RowBox[{
     RowBox[{"Range", "[", 
      RowBox[{"1", ",", " ", "2"}], "]"}], ",", " ", 
     RowBox[{
      RowBox[{
       RowBox[{"Cases", "[", 
        RowBox[{"pos", ",", " ", 
         RowBox[{"Point", "[", 
          RowBox[{"{", 
           RowBox[{"#", ",", " ", "_", ",", " ", "_"}], "}"}], "]"}]}], "]"}],
        "!=", 
       RowBox[{"{", "}"}]}], "&"}]}], "]"}]}], ";"}], "\n", 
 RowBox[{
  RowBox[{"xplanes", " ", "=", " ", 
   RowBox[{
    RowBox[{
     RowBox[{"ParametricPlot3D", "[", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{"#", ",", " ", "u", ",", " ", "v"}], "}"}], ",", " ", 
       RowBox[{"{", 
        RowBox[{"u", ",", " ", 
         RowBox[{"1", "-", "extra"}], ",", " ", 
         RowBox[{"2", "+", "extra"}]}], "}"}], ",", " ", 
       RowBox[{"{", 
        RowBox[{"v", ",", " ", 
         RowBox[{"1", "-", "extra"}], ",", " ", 
         RowBox[{"2", "+", "extra"}]}], "}"}], ",", 
       RowBox[{"PlotStyle", "\[Rule]", 
        RowBox[{"{", 
         RowBox[{
          RowBox[{"Lighter", "[", "Blue", "]"}], ",", " ", 
          RowBox[{"Opacity", "[", "0.25", "]"}]}], "}"}]}], ",", " ", 
       RowBox[{"Mesh", "->", "None"}]}], "]"}], "&"}], "/@", "xcoords"}]}], 
  ";"}], "\n", 
 RowBox[{
  RowBox[{"ycoords", "=", 
   RowBox[{"Select", "[", 
    RowBox[{
     RowBox[{"Range", "[", 
      RowBox[{"1", ",", " ", "2"}], "]"}], ",", " ", 
     RowBox[{
      RowBox[{
       RowBox[{"Cases", "[", 
        RowBox[{"pos", ",", " ", 
         RowBox[{"Point", "[", 
          RowBox[{"{", 
           RowBox[{"_", ",", " ", "#", ",", " ", "_"}], "}"}], "]"}]}], "]"}],
        "!=", 
       RowBox[{"{", "}"}]}], "&"}]}], "]"}]}], ";"}], "\n", 
 RowBox[{
  RowBox[{"yplanes", "=", 
   RowBox[{
    RowBox[{
     RowBox[{"ParametricPlot3D", "[", 
      RowBox[{
       RowBox[{"{", 
        RowBox[{"u", ",", "#", ",", " ", "v"}], "}"}], ",", " ", 
       RowBox[{"{", 
        RowBox[{"u", ",", " ", 
         RowBox[{"1", "-", "extra"}], ",", " ", 
         RowBox[{"2", "+", "extra"}]}], "}"}], ",", " ", 
       RowBox[{"{", 
        RowBox[{"v", ",", " ", 
         RowBox[{"1", "-", "extra"}], ",", " ", 
         RowBox[{"2", "+", "extra"}]}], "}"}], ",", 
       RowBox[{"PlotStyle", "\[Rule]", 
        RowBox[{"{", 
         RowBox[{"Red", ",", " ", 
          RowBox[{"Opacity", "[", "0.25", "]"}]}], "}"}]}], ",", " ", 
       RowBox[{"Mesh", "->", "None"}]}], "]"}], "&"}], "/@", "ycoords"}]}], 
  ";"}], "\n", 
 RowBox[{
  RowBox[{"zcoords", "=", 
   RowBox[{"Select", "[", 
    RowBox[{
     RowBox[{"Range", "[", 
      RowBox[{"1", ",", " ", "2"}], "]"}], ",", " ", 
     RowBox[{
      RowBox[{
       RowBox[{"Cases", "[", 
        RowBox[{"pos", ",", " ", 
         RowBox[{"Point", "[", 
          RowBox[{"{", 
           RowBox[{"_", ",", " ", "_", ",", " ", "#"}], "}"}], "]"}]}], "]"}],
        "!=", 
       RowBox[{"{", "}"}]}], "&"}]}], "]"}]}], ";"}], "\n", 
 RowBox[{
  RowBox[{
   RowBox[{"zplanes", " ", "=", " ", 
    RowBox[{
     RowBox[{
      RowBox[{"ParametricPlot3D", "[", 
       RowBox[{
        RowBox[{"{", 
         RowBox[{"u", ",", "v", ",", " ", "#"}], "}"}], ",", "  ", 
        RowBox[{"{", 
         RowBox[{"u", ",", " ", 
          RowBox[{"1", "-", "extra"}], ",", " ", 
          RowBox[{"2", "+", "extra"}]}], "}"}], ",", " ", 
        RowBox[{"{", 
         RowBox[{"v", ",", " ", 
          RowBox[{"1", "-", "extra"}], ",", " ", 
          RowBox[{"2", "+", "extra"}]}], "}"}], ",", 
        RowBox[{"PlotStyle", "\[Rule]", 
         RowBox[{"{", 
          RowBox[{"Green", ",", " ", 
           RowBox[{"Opacity", "[", "0.25", "]"}]}], "}"}]}], ",", " ", 
        RowBox[{"Mesh", "->", "None"}]}], "]"}], "&"}], "/@", "zcoords"}]}], 
   ";"}], "\n"}], "\[IndentingNewLine]", 
 RowBox[{"Show", "[", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{
    "zplanes", ",", " ", "xplanes", ",", " ", "yplanes", ",", " ", "dots"}], 
    "}"}], ",", " ", 
   RowBox[{"PlotRange", "\[Rule]", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"{", 
       RowBox[{".9", ",", " ", "2.1"}], "}"}], ",", " ", 
      RowBox[{"{", 
       RowBox[{".9", ",", " ", "2.1"}], "}"}], ",", " ", 
      RowBox[{"{", 
       RowBox[{".9", ",", " ", "2.1"}], "}"}]}], "}"}]}], ",", 
   RowBox[{"Ticks", "\[Rule]", "None"}]}], "]"}]}], "Input",
 CellLabel->"In[5]:=",ExpressionUUID->"a1fb797b-c257-479c-97f6-9b11f3a40ff6"],

Cell[BoxData[
 Graphics3DBox[{{GraphicsComplex3DBox[CompressedData["
1:eJx12DuLFFkYgOGencBENhMjQaHBxEvmBQTHwGDSNTIVNxBtDQR/gYIgJi0I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     "], {
      {RGBColor[0, 1, 0], Opacity[0.25], EdgeForm[None], 
       StyleBox[GraphicsGroup3DBox[
         TagBox[Polygon3DBox[CompressedData["
1:eJwBCQX2+iFib1JiAgAAAKgBAAADAAAA4gIRFQUGEgIDEwMEFgYHFwcIGgoL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           "]],
          Annotation[#, "Charting`Private`Tag$3524#1"]& ]],
        Lighting->Automatic]}, {}, {}, {}, {}},
     VertexNormals->CompressedData["
1:eJztyLENABAUQMEfJjGJHYwgUVtdq6MXG9xLXnOlzzZSROx7jl+rcs4555xz
zjnnnHPOOef89QMOQClu
      "]], {}}, {GraphicsComplex3DBox[CompressedData["
1:eJx12DGLVFcYgOHZWNhIOtlqIcKATdQuGhB2Ulhsq1VaMYXomCLgL1AIiM0E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     "], {
      {RGBColor[0, 1, 0], Opacity[0.25], EdgeForm[None], 
       StyleBox[GraphicsGroup3DBox[
         TagBox[Polygon3DBox[CompressedData["
1:eJwBCQX2+iFib1JiAgAAAKgBAAADAAAA4gIRFQUGEgIDEwMEFgYHFwcIGgoL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           "]],
          Annotation[#, "Charting`Private`Tag$3543#1"]& ]],
        Lighting->Automatic]}, {}, {}, {}, {}},
     VertexNormals->CompressedData["
1:eJztyLENABAUQMEfJjGJHYwgUVtdq6MXG9xLXnOlzzZSROx7jl+rcs4555xz
zjnnnHPOOef89QMOQClu
      "]], {}}, {GraphicsComplex3DBox[CompressedData["
1:eJx12D2LVGcYgOFZLdIEO9lKUBiw8aPTCELWwmJbrWxFC9HRQvAXJCBImhEC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     "], {
      {RGBColor[
        NCache[
         Rational[1, 3], 0.3333333333333333], 
        NCache[
         Rational[1, 3], 0.3333333333333333], 1], Opacity[0.25], EdgeForm[
       None], 
       StyleBox[GraphicsGroup3DBox[
         TagBox[Polygon3DBox[CompressedData["
1:eJwBCQX2+iFib1JiAgAAAKgBAAADAAAA4gIRFQUGEgIDEwMEFgYHFwcIGgoL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           "]],
          Annotation[#, "Charting`Private`Tag$3399#1"]& ]],
        Lighting->Automatic]}, {}, {}, {}, {}},
     VertexNormals->CompressedData["
1:eJztyLEJwCAARcFPnMRJsoMjCNaubmuXNEKKjHAPXnO1zzauJPu95LTu/MY5
55xzzjnnnHPOOeec828Per4pbg==
      "]], {}}, {
    GraphicsComplex3DBox[CompressedData["
1:eJx12D+LVFccgOHZWNhIOtlqIcKATdROIwR2LSy21SqtaCE6sRD8BAkIYjOC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     "], {
      {RGBColor[
        NCache[
         Rational[1, 3], 0.3333333333333333], 
        NCache[
         Rational[1, 3], 0.3333333333333333], 1], Opacity[0.25], EdgeForm[
       None], 
       StyleBox[GraphicsGroup3DBox[
         TagBox[Polygon3DBox[CompressedData["
1:eJwBCQX2+iFib1JiAgAAAKgBAAADAAAA4gIRFQUGEgIDEwMEFgYHFwcIGgoL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           "]],
          Annotation[#, "Charting`Private`Tag$3467#1"]& ]],
        Lighting->Automatic]}, {}, {}, {}, {}},
     VertexNormals->CompressedData["
1:eJztyLEJwCAARcFPnMRJsoMjCNaubmuXNEKKjHAPXnO1zzauJPu95LTu/MY5
55xzzjnnnHPOOeec828Per4pbg==
      "]], {}}, {
    GraphicsComplex3DBox[CompressedData["
1:eJx12D2LVGcYgOExFjaSLlgtKAzYaOz8gMAmRYppY2UbtBCdWAj5BQqC2IwQ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     "], {
      {RGBColor[1, 0, 0], Opacity[0.25], EdgeForm[None], 
       StyleBox[GraphicsGroup3DBox[
         TagBox[Polygon3DBox[CompressedData["
1:eJwBCQX2+iFib1JiAgAAAKgBAAADAAAA4gIRFQUGEgIDEwMEFgYHFwcIGgoL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           "]],
          Annotation[#, "Charting`Private`Tag$3486#1"]& ]],
        Lighting->Automatic]}, {}, {}, {}, {}},
     VertexNormals->CompressedData["
1:eJztyKENACEQAMELVEJLlECCpkRawuJAIf5bmE3WTGmj9hQR+57j25o/4pxz
zjnnnHPOOeecc8758wNKE6Xu
      "]], {}}, {GraphicsComplex3DBox[CompressedData["
1:eJx12DuLk2kYgOHoFDZiJ1aCQsDGQ+cBBLWwmHa3shUtRKOF4C9QEMQmgqCC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     "], {
      {RGBColor[1, 0, 0], Opacity[0.25], EdgeForm[None], 
       StyleBox[GraphicsGroup3DBox[
         TagBox[Polygon3DBox[CompressedData["
1:eJwBCQX2+iFib1JiAgAAAKgBAAADAAAA4gIRFQUGEgIDEwMEFgYHFwcIGgoL
HAwNGAgJGQkKFAQFKhobGwsMKRkaIxMUIBARIRESJBQVJRUWKBgZ7+XkJhYX
JxcYHQ0OKxscLBwdPy8wRzc4MSEiLR0eMiIjNCQlNycoMyMkNSUmNiYnLx8g
MCAhOCgpOSkqQDAxPCwtPi4vQTEyIhITQjIzRDQ1OiorOyssQzM0RTU2gHBx
RjY3f29wTj4/Sjo7Szs8Tz9AUEBBU0NEVUVGUUFCUkJDTT0+Y1NUVERFYlJT
XExNWEhJWUlKXU1OXk5PYVFSV0dIX09QYFBRVkZHZFRVZVVWd2doSTk6aVla
ZlZXa1tcbV1ecGBhbFxdbl5fb19gZ1dYaFhZcWFicmJjeGhpdWVmdmZnempr
SDg5e2tsfW1uc2NkdGRlfGxtfm5vWkpLgXFyzb2+hnZ3g3N0hHR1nIyNh3d4
inp7i3t8jHx9jX1+hXV2iXl6jn5/kICBlYWGkoKDk4OEloaHmIiJm4uMkYGC
mYmKmoqLj3+A8PjnnY2On4+Qo5OUoJCRoZGSno6PpJSVp5eYqJiZqZmaqpqb
opKTq5ucrJydrZ2er5+gsKChsaGisqKjlISFs6OkuKiprp6ftqant6eotKSl
gnJzuamqu6uswLCxva2uvq6vwbGywrKzxra3yLi5w7O0xbW2v6+w1sbHx7e4
1cXGzr6/y7u8zLy9z7/A0MDB5sXUyrq70cHC0sLDybm618fI2MjJCBgXvKyt
3MzN2cnK3c3O38/Q4+IQ3s7P4NDR7ejS2srL28vMAhIRAxMSCRkYBhYVBxcW
ChoZuqqrCxsaDR0cBBQTBRUUDBwb5B0OECAfESEgEiIhFCQjFSUkFiYlFycm
GCgnGSkoGiopGysqHCwrHS0sHy8uIDAvITEwIjIxIzMyJDQzJTU0JjY1Jzc2
KDg3KTk4Kjo5Kzs6LDw7Lj49Lz8+M0NCMEA/MUFASVlYNERDNkZFN0dGOEhH
OUlIMkJBOkpJO0tKPU1MP09OQFBPQVFQQlJRSFhXQ1NSR1dWPk5NRVVURlZV
RFRTNUVESlpZbn59TV1cTl5dT19eUGBfUWFgUmJhU2NiVGRjVWVkVmZlV2dm
WGhnWWloW2tqXGxrXW1sXm5tX29uYHBvYXFwYnJxY3NyZHRzZXV0ZnZ1Z3d2
bHx7aHh3anp5TFxbbX18b39+cIB/cYGAcoKBa3t6c4OCdISDdYWEd4eGeYmI
eoqJe4uKgZGQfIyLgJCPdoaFfo6Nf4+OfY2MEyMigpKRhJSTiZmYhZWUhpaV
ipqZi5uajp6dkKCfjJybjZ2ciJiXnq6tj5+ena2sl6emk6OilKSjmKinmamo
nKyrkqKhmqqpm6uqkaGgn6+uoLCvssLBu8vKpLSzobGwpra1qLi3q7u6p7e2
qbm4qrq5orKxo7OyrLy7rb28s8PCsMC/scHAtcXElaWktsbFuMjHrr69r7++
t8fGucnIusrJvMzLg5OSwdHQvs7Nv8/OwtLR8Ofmx9fWydnYxdXUxtbVwNDP
yNjXytrZ6+QOzNzbzd3czt7dz9/eHeQe0ODf8u7jy9va7uriEOIR6ODRpZWW
5OUe+fHhvc3M8eno7ObU6Ong8+/r9u4B4uoC9PDs9fHt5ufE0ujR4+7i9+8P
7vIB7PDm7fHo7/MPxebE8PTT7vbq6+/k+PDT8fXh7/fl8fnpl2heKQ==
           "]],
          Annotation[#, "Charting`Private`Tag$3505#1"]& ]],
        Lighting->Automatic]}, {}, {}, {}, {}},
     VertexNormals->CompressedData["
1:eJztyKENACEQAMELVEJLlECCpkRawuJAIf5bmE3WTGmj9hQR+57j25o/4pxz
zjnnnHPOOeecc8758wNKE6Xu
      "]], {}}, 
   {RGBColor[1, 0, 0], PointSize[
    0.06], {Point3DBox[{1, 1, 1}], Point3DBox[{2, 2, 2}]}, 
    {RGBColor[
      NCache[
       Rational[1, 3], 0.3333333333333333], 
      NCache[
       Rational[1, 3], 0.3333333333333333], 1], Point3DBox[{1, 1, 2}], 
     Point3DBox[{1, 2, 1}], Point3DBox[{1, 2, 2}]}, 
    {GrayLevel[0], Point3DBox[{2, 1, 1}], Point3DBox[{2, 1, 2}], 
     Point3DBox[{2, 2, 1}]}}},
  Axes->True,
  DisplayFunction->Identity,
  FaceGridsStyle->Automatic,
  ImagePadding->Automatic,
  ImageSize->{377.1589333800912, 356.838325097973},
  ImageSizeRaw->Automatic,
  Method->{
   "DefaultGraphicsInteraction" -> {
     "Version" -> 1.2, "TrackMousePosition" -> {True, False}, 
      "Effects" -> {
       "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, 
        "Droplines" -> {
         "freeformCursorMode" -> True, 
          "placement" -> {"x" -> "All", "y" -> "None"}}}}},
  PlotRange->{{0.9, 2.1}, {0.9, 2.1}, {0.9, 2.1}},
  PlotRangePadding->{{
     Scaled[0.05], 
     Scaled[0.05]}, {
     Scaled[0.05], 
     Scaled[0.05]}, {
     Scaled[0.05], 
     Scaled[0.05]}},
  Ticks->None,
  ViewPoint->{3.1509193686905808`, 1.1461419689331056`, 0.45614221363594165`},
  
  ViewVertical->{0.49198632496605194`, 0.04644941787093437, 
   0.8693629320518846}]], "Output",
 CellLabel->"Out[13]=",ExpressionUUID->"cfb751c4-bb6e-4007-8123-a18256c1616d"]
}, Open  ]]
}, Open  ]]
},
WindowSize->{1291, 1096},
WindowMargins->{{137, Automatic}, {Automatic, 66}},
FrontEndVersion->"12.1 for Mac OS X x86 (64-bit) (March 18, 2020)",
StyleDefinitions->"Default.nb",
ExpressionUUID->"f6151892-af4d-4399-a7a9-dc160aa2a1bc"
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[558, 20, 146, 2, 46, "Input",ExpressionUUID->"18bb20ad-2eca-4536-820b-83197ca20997"],
Cell[707, 24, 138, 2, 46, "Input",ExpressionUUID->"56b70a0d-2237-4ef0-8b07-9874ffdc09ee"],
Cell[848, 28, 920, 24, 109, "Input",ExpressionUUID->"e8f277a8-95c5-4a68-8b8c-e621b0ab63a3"],
Cell[1771, 54, 717, 18, 78, "Input",ExpressionUUID->"4b199021-aa3f-498f-bafc-ffa1babeae44"],
Cell[2491, 74, 112, 0, 53, "Text",ExpressionUUID->"2d851b6b-9e09-4f49-b69b-41a3f3e99bb1"],
Cell[2606, 76, 3422, 99, 388, "Input",ExpressionUUID->"54b2a133-23e2-482a-b05a-d2e5a07d5c26"],
Cell[6031, 177, 627, 17, 78, "Input",ExpressionUUID->"cbe629c7-ccf9-4804-8c5b-383339583d90"],
Cell[CellGroupData[{
Cell[6683, 198, 91, 0, 67, "Subsubsection",ExpressionUUID->"60b6e213-e296-4c53-88b4-78a4a54c747e"],
Cell[6777, 200, 1119, 31, 109, "Input",ExpressionUUID->"7867bf1b-b945-4f6f-b14d-eb8f8d30d6ba"],
Cell[CellGroupData[{
Cell[7921, 235, 107, 1, 46, "Input",ExpressionUUID->"9d2a2d95-4543-441d-8393-e55318779207"],
Cell[8031, 238, 963, 27, 84, "Output",ExpressionUUID->"2ff3130b-83d0-40c9-8366-a2f84b40778f"]
}, Open  ]],
Cell[CellGroupData[{
Cell[9031, 270, 5834, 167, 605, "Input",ExpressionUUID->"a1fb797b-c257-479c-97f6-9b11f3a40ff6"],
Cell[14868, 439, 21399, 399, 561, "Output",ExpressionUUID->"cfb751c4-bb6e-4007-8123-a18256c1616d"]
}, Open  ]]
}, Open  ]]
}
]
*)