(* Content-type: application/mathematica *)

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

(* CreatedBy='Mathematica 7.0' *)

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   DynamicModuleBox[{$CellContext`a$$ = 0.5, $CellContext`av$$ = 
    0, $CellContext`aw$$ = 0, $CellContext`b$$ = 0.5, $CellContext`bv$$ = 2 
    Pi, $CellContext`bw$$ = Pi, $CellContext`c$$ = 0.5, $CellContext`FIELD$$ =
     True, $CellContext`n$$ = 20, $CellContext`PLOT$$ = 
    True, $CellContext`q$$ = 0.8, $CellContext`s$$ = Rational[2, 5] 
    Pi, $CellContext`t$$ = Rational[3, 2] Pi, Typeset`show$$ = True, 
    Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", 
    Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = 
    "\"untitled\"", Typeset`specs$$ = {{{
       Hold[$CellContext`t$$], Rational[3, 2] Pi, 
       Style["u", 13, Bold]}, 0, 2 Pi}, {{
       Hold[$CellContext`s$$], Rational[1, 2] Pi, 
       Style["v", 13, Bold]}, 0.001, Pi}, {
      Hold[
       Style["                                u cut", 13, Bold]], 
      Manipulate`Dump`ThisIsNotAControl}, {{
       Hold[$CellContext`av$$], 0, 
       Style["", 13, Bold]}, 0, 2 Pi}, {{
       Hold[$CellContext`bv$$], 2 Pi, 
       Style["", 13, Bold]}, 0, 2 Pi}, {
      Hold[
       Style["                                v cut", 13, Bold]], 
      Manipulate`Dump`ThisIsNotAControl}, {{
       Hold[$CellContext`aw$$], 0, 
       Style["", 13, Bold]}, 0, Pi}, {{
       Hold[$CellContext`bw$$], Pi, 
       Style["", 13, Bold]}, 0, Pi}, {
      Hold[
       Style["    Plot", 13, Bold]], Manipulate`Dump`ThisIsNotAControl}, {{
       Hold[$CellContext`PLOT$$], True, ""}, {True, False}}, {
      Hold[
       Style["    Field", 13, Bold, 
        RGBColor[0, 0, 1]]], Manipulate`Dump`ThisIsNotAControl}, {{
       Hold[$CellContext`FIELD$$], True, ""}, {True, False}}, {
      Hold[
       Style["                                Density", 13, Bold]], 
      Manipulate`Dump`ThisIsNotAControl}, {{
       Hold[$CellContext`n$$], 20, 
       Style["", 13, Bold]}, 1, 100, 5}, {
      Hold[
       Style["                                Opacity", 13, Bold]], 
      Manipulate`Dump`ThisIsNotAControl}, {{
       Hold[$CellContext`q$$], 0.8, 
       Style["", 13, Bold]}, 0, 1}, {{
       Hold[$CellContext`a$$], 0.5, 
       Style[
       "\!\(\*\nStyleBox[\"a\",\nFontColor->RGBColor[0, 0, 1]]\)", 13, 
        Bold]}, -1, 1}, {{
       Hold[$CellContext`b$$], 0.5, 
       Style[
       "\!\(\*\nStyleBox[\"b\",\nFontColor->RGBColor[0, 0, 1]]\)", 13, 
        Bold]}, -1, 1}, {{
       Hold[$CellContext`c$$], 0.5, 
       Style[
       "\!\(\*\nStyleBox[\"c\",\nFontColor->RGBColor[0, 0, 1]]\)", 13, 
        Bold]}, -1, 1}, {
      Hold[
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          Style[
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1]]\)\!\(\*\nStyleBox[\" \",\nFontColor->RGBColor[0, 0, 1]]\)\!\(\*\n\
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            Style[
            "\!\(\*\nStyleBox[OverscriptBox[\n  StyleBox[\"F\",\n\
FontColor->RGBColor[0, 0, 1]], \"\[RightVector]\"],\nFontColor->RGBColor[0, \
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StyleBox[\"a\",\nFontColor->RGBColor[0, 0, 1]]\)x,\!\(\*\nStyleBox[\"b\",\n\
FontColor->RGBColor[0, 0, 1]]\)y,\!\(\*\nStyleBox[\"c\",\n\
FontColor->RGBColor[0, 0, 1]]\)z}=", 15, Bold], 
            Style[
             $CellContext`F[{$CellContext`x, $CellContext`y, $CellContext`z}, \
$CellContext`a$$, $CellContext`b$$, $CellContext`c$$], 15, Bold]}], Null, 
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          Style["Outward Unit Normal", 15, Red, Bold], 
          Row[{
            Style[
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            Style[
             $CellContext`Nr[$CellContext`u, $CellContext`v], 15, Red, 
             Bold]}], Null, Null, 
          Style[
          "Outward flux of \!\(\*\nStyleBox[OverscriptBox[\n  StyleBox[\"F\",\
\nFontColor->RGBColor[0, 0, 1]], \"\[RightVector]\"],\nFontColor->RGBColor[0, \
0, 1]]\) through the sphere", 15, Bold], 
          Row[{
            Style[
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StyleBox[\"F\",\nFontColor->RGBColor[0, 0, 1]], \"\[RightVector]\"],\n\
FontColor->RGBColor[0, 0, 1]]\)\[CenterDot]\!\(\*\nStyleBox[OverscriptBox[\n  \
StyleBox[\"n\",\nFontColor->RGBColor[1, 0, 0]], \"\[RightVector]\"],\n\
FontColor->RGBColor[1, 0, 0]]\) dS=", 15, Bold], 
            
            Style[(4/
              3) ($CellContext`a$$ + $CellContext`b$$ + $CellContext`c$$) Pi, 
             15, Bold]}]}, Center]]], Manipulate`Dump`ThisIsNotAControl}}, 
    Typeset`size$$ = {710., {352., 358.}}, Typeset`update$$ = 0, 
    Typeset`initDone$$, Typeset`skipInitDone$$ = 
    False, $CellContext`t$3819$$ = 0, $CellContext`s$3820$$ = 
    0, $CellContext`av$3821$$ = 0, $CellContext`bv$3822$$ = 
    0, $CellContext`aw$3823$$ = 0, $CellContext`bw$3824$$ = 
    0, $CellContext`PLOT$3825$$ = False, $CellContext`FIELD$3826$$ = 
    False, $CellContext`n$3827$$ = 0, $CellContext`q$3828$$ = 
    0, $CellContext`a$3829$$ = 0, $CellContext`b$3830$$ = 0}, 
    DynamicBox[Manipulate`ManipulateBoxes[
     1, StandardForm, 
      "Variables" :> {$CellContext`a$$ = 0.5, $CellContext`av$$ = 
        0, $CellContext`aw$$ = 0, $CellContext`b$$ = 0.5, $CellContext`bv$$ = 
        2 Pi, $CellContext`bw$$ = Pi, $CellContext`c$$ = 
        0.5, $CellContext`FIELD$$ = True, $CellContext`n$$ = 
        20, $CellContext`PLOT$$ = True, $CellContext`q$$ = 
        0.8, $CellContext`s$$ = Rational[1, 2] Pi, $CellContext`t$$ = 
        Rational[3, 2] Pi}, "ControllerVariables" :> {
        Hold[$CellContext`t$$, $CellContext`t$3819$$, 0], 
        Hold[$CellContext`s$$, $CellContext`s$3820$$, 0], 
        Hold[$CellContext`av$$, $CellContext`av$3821$$, 0], 
        Hold[$CellContext`bv$$, $CellContext`bv$3822$$, 0], 
        Hold[$CellContext`aw$$, $CellContext`aw$3823$$, 0], 
        Hold[$CellContext`bw$$, $CellContext`bw$3824$$, 0], 
        Hold[$CellContext`PLOT$$, $CellContext`PLOT$3825$$, False], 
        Hold[$CellContext`FIELD$$, $CellContext`FIELD$3826$$, False], 
        Hold[$CellContext`n$$, $CellContext`n$3827$$, 0], 
        Hold[$CellContext`q$$, $CellContext`q$3828$$, 0], 
        Hold[$CellContext`a$$, $CellContext`a$3829$$, 0], 
        Hold[$CellContext`b$$, $CellContext`b$3830$$, 0]}, 
      "OtherVariables" :> {
       Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, 
        Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, 
        Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$,
         Typeset`skipInitDone$$}, 
      "Body" :> ($CellContext`SDB = ParametricPlot3D[
          $CellContext`Surf[$CellContext`v, $CellContext`w], {$CellContext`v, \
$CellContext`av$$, $CellContext`bv$$}, {$CellContext`w, $CellContext`aw$$, \
$CellContext`bw$$}, PlotStyle -> Opacity[$CellContext`q$$], PlotLabel -> 
          Style["Unit Sphere:  \!\(\*OverscriptBox[\(r\), \(\[RightVector]\)]\
\)(u,v)={Cos[u] Sin[v], Sin[u] Sin[v], Cos[v]}", 15, Bold]]; $CellContext`NR = 
        Graphics3D[{Red, Arrowheads -> Small, 
           Arrow[{
             $CellContext`Surf[$CellContext`t$$, $CellContext`s$$], \
$CellContext`Surf[$CellContext`t$$, $CellContext`s$$] + \
$CellContext`Nr[$CellContext`t$$, $CellContext`s$$]}]}]; $CellContext`Fld = 
        Graphics3D[{Blue, Arrowheads -> Small, 
           Arrow[{
             $CellContext`Surf[$CellContext`t$$, $CellContext`s$$], \
$CellContext`Surf[$CellContext`t$$, $CellContext`s$$] + $CellContext`F[
               $CellContext`Surf[$CellContext`t$$, $CellContext`s$$], \
$CellContext`a$$, $CellContext`b$$, $CellContext`c$$]}]}]; \
$CellContext`NrPlot = Flatten[
          Table[
           Graphics3D[{Red, Arrowheads -> Small, 
             Arrow[{
               $CellContext`Surf[$CellContext`Av + (($CellContext`Bv - \
$CellContext`Av)/$CellContext`n$$) $CellContext`i, $CellContext`Aw + \
(($CellContext`Bw - $CellContext`Aw)/$CellContext`n$$) $CellContext`j], \
$CellContext`Surf[$CellContext`Av + (($CellContext`Bv - \
$CellContext`Av)/$CellContext`n$$) $CellContext`i, $CellContext`Aw + \
(($CellContext`Bw - $CellContext`Aw)/$CellContext`n$$) $CellContext`j] + \
$CellContext`Nr[$CellContext`Av + (($CellContext`Bv - \
$CellContext`Av)/$CellContext`n$$) $CellContext`i, $CellContext`Aw + \
(($CellContext`Bw - $CellContext`Aw)/$CellContext`n$$) $CellContext`j]}]}], \
{$CellContext`i, 1, $CellContext`n$$}, {$CellContext`j, $CellContext`n$$}], 
          2]; $CellContext`FPlot = Flatten[
          Table[
           Graphics3D[{Blue, Arrowheads -> Small, 
             Arrow[{
               $CellContext`Surf[$CellContext`Av + (($CellContext`Bv - \
$CellContext`Av)/$CellContext`n$$) $CellContext`i, $CellContext`Aw + \
(($CellContext`Bw - $CellContext`Aw)/$CellContext`n$$) $CellContext`j], \
$CellContext`Surf[$CellContext`Av + (($CellContext`Bv - \
$CellContext`Av)/$CellContext`n$$) $CellContext`i, $CellContext`Aw + \
(($CellContext`Bw - $CellContext`Aw)/$CellContext`n$$) $CellContext`j] + \
$CellContext`F[
                 $CellContext`Surf[$CellContext`Av + (($CellContext`Bv - \
$CellContext`Av)/$CellContext`n$$) $CellContext`i, $CellContext`Aw + \
(($CellContext`Bw - $CellContext`Aw)/$CellContext`n$$) $CellContext`j], \
$CellContext`a$$, $CellContext`b$$, $CellContext`c$$]}]}], {$CellContext`i, 
            1, $CellContext`n$$}, {$CellContext`j, $CellContext`n$$}], 2]; 
       If[$CellContext`PLOT$$, 
         If[$CellContext`FIELD$$, 
          Framed[
           
           Show[$CellContext`SDB, $CellContext`FPlot, $CellContext`NrPlot, 
            PlotRange -> {{-2, 2}, {-2, 2}, {-2, 2}}, 
            ImageSize -> {700, 700}]], 
          Framed[
           
           Show[$CellContext`SDB, $CellContext`NrPlot, 
            PlotRange -> {{-2, 2}, {-2, 2}, {-2, 2}}, 
            ImageSize -> {700, 700}]]], 
         Framed[
          
          Show[$CellContext`SDB, $CellContext`Fld, $CellContext`NR, 
           PlotRange -> {{-2, 2}, {-2, 2}, {-2, 2}}, 
           ImageSize -> {700, 700}]]]), 
      "Specifications" :> {{{$CellContext`t$$, Rational[3, 2] Pi, 
          Style["u", 13, Bold]}, 0, 2 
         Pi}, {{$CellContext`s$$, Rational[1, 2] Pi, 
          Style["v", 13, Bold]}, 0.001, Pi}, Delimiter, 
        Style[
        "                                u cut", 13, 
         Bold], {{$CellContext`av$$, 0, 
          Style["", 13, Bold]}, 0, 2 Pi}, {{$CellContext`bv$$, 2 Pi, 
          Style["", 13, Bold]}, 0, 2 Pi}, Delimiter, 
        Style[
        "                                v cut", 13, 
         Bold], {{$CellContext`aw$$, 0, 
          Style["", 13, Bold]}, 0, Pi}, {{$CellContext`bw$$, Pi, 
          Style["", 13, Bold]}, 0, Pi}, Delimiter, 
        Style[
        "    Plot", 13, Bold], {{$CellContext`PLOT$$, True, ""}, {
         True, False}}, 
        Style["    Field", 13, Bold, 
         RGBColor[0, 0, 1]], {{$CellContext`FIELD$$, True, ""}, {
         True, False}}, 
        Style[
        "                                Density", 13, 
         Bold], {{$CellContext`n$$, 20, 
          Style["", 13, Bold]}, 1, 100, 5}, 
        Style[
        "                                Opacity", 13, 
         Bold], {{$CellContext`q$$, 0.8, 
          Style["", 13, Bold]}, 0, 1}, Delimiter, {{$CellContext`a$$, 0.5, 
          Style[
          "\!\(\*\nStyleBox[\"a\",\nFontColor->RGBColor[0, 0, 1]]\)", 13, 
           Bold]}, -1, 1}, {{$CellContext`b$$, 0.5, 
          Style[
          "\!\(\*\nStyleBox[\"b\",\nFontColor->RGBColor[0, 0, 1]]\)", 13, 
           Bold]}, -1, 1}, {{$CellContext`c$$, 0.5, 
          Style[
          "\!\(\*\nStyleBox[\"c\",\nFontColor->RGBColor[0, 0, 1]]\)", 13, 
           Bold]}, -1, 1}, 
        Dynamic[
         Column[{
           Style[
           "\!\(\*\nStyleBox[\"Vector\",\nFontColor->RGBColor[0, 0, 1]]\)\!\(\
\*\nStyleBox[\" \",\nFontColor->RGBColor[0, 0, 1]]\)\!\(\*\n\
StyleBox[\"Field\",\nFontColor->RGBColor[0, 0, 1]]\)", 15, Bold], 
           Row[{
             Style[
             "\!\(\*\nStyleBox[OverscriptBox[\n  StyleBox[\"F\",\n\
FontColor->RGBColor[0, 0, 1]], \"\[RightVector]\"],\nFontColor->RGBColor[0, \
0, 1]]\)\!\(\*\nStyleBox[\"(\",\nFontColor->GrayLevel[0]]\)x,y,z)={\!\(\*\n\
StyleBox[\"a\",\nFontColor->RGBColor[0, 0, 1]]\)x,\!\(\*\nStyleBox[\"b\",\n\
FontColor->RGBColor[0, 0, 1]]\)y,\!\(\*\nStyleBox[\"c\",\n\
FontColor->RGBColor[0, 0, 1]]\)z}=", 15, Bold], 
             Style[
              $CellContext`F[{$CellContext`x, $CellContext`y, \
$CellContext`z}, $CellContext`a$$, $CellContext`b$$, $CellContext`c$$], 15, 
              Bold]}], Null, Null, Null, Null, 
           Style["Outward Unit Normal", 15, Red, Bold], 
           Row[{
             Style[
             "\!\(\*OverscriptBox[\(n\), \(\[Rule]\)]\)[u,v]=", 15, Red, 
              Bold], 
             Style[
              $CellContext`Nr[$CellContext`u, $CellContext`v], 15, Red, 
              Bold]}], Null, Null, 
           Style[
           "Outward flux of \!\(\*\nStyleBox[OverscriptBox[\n  \
StyleBox[\"F\",\nFontColor->RGBColor[0, 0, 1]], \"\[RightVector]\"],\n\
FontColor->RGBColor[0, 0, 1]]\) through the sphere", 15, Bold], 
           Row[{
             Style[
             "\[Integral]\[Integral]\!\(\*\nStyleBox[OverscriptBox[\n  \
StyleBox[\"F\",\nFontColor->RGBColor[0, 0, 1]], \"\[RightVector]\"],\n\
FontColor->RGBColor[0, 0, 1]]\)\[CenterDot]\!\(\*\nStyleBox[OverscriptBox[\n  \
StyleBox[\"n\",\nFontColor->RGBColor[1, 0, 0]], \"\[RightVector]\"],\n\
FontColor->RGBColor[1, 0, 0]]\) dS=", 15, Bold], 
             
             Style[(4/
               3) ($CellContext`a$$ + $CellContext`b$$ + $CellContext`c$$) Pi,
               15, Bold]}]}, Center]]}, 
      "Options" :> {
       ControlPlacement -> Left, FrameLabel -> 
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\" \",\nFontColor->RGBColor[0, 0, 1]]\)\!\(\*\nStyleBox[\"N\",\n\
FontColor->RGBColor[0, 0, 1]]\)\!\(\*\nStyleBox[\".\",\n\
FontColor->RGBColor[0, 0, 1]]\)\!\(\*\nStyleBox[\" \",\n\
FontColor->RGBColor[0, 0, 1]]\)\!\(\*\nStyleBox[\"Bykov\",\n\
FontColor->RGBColor[0, 0, 1]]\)\!\(\*\nStyleBox[\",\",\n\
FontColor->RGBColor[0, 0, 1]]\)\!\(\*\nStyleBox[\" \",\n\
FontColor->RGBColor[0, 0, 1]]\)\!\(\*\nStyleBox[\"SJ\",\n\
FontColor->RGBColor[0, 0, 1]]\)\!\(\*\nStyleBox[\" \",\n\
FontColor->RGBColor[0, 0, 1]]\)\!\(\*\nStyleBox[\"Delta\",\n\
FontColor->RGBColor[0, 0, 1]]\)\!\(\*\nStyleBox[\" \",\n\
FontColor->RGBColor[0, 0, 1]]\)\!\(\*\nStyleBox[\"College\",\n\
FontColor->RGBColor[0, 0, 1]]\)"}, "DefaultOptions" :> {}],
     ImageSizeCache->{1072., {391., 396.}},
     SingleEvaluation->True],
    Deinitialization:>None,
    DynamicModuleValues:>{},
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             "]], {
           Axes -> True, PlotLabel -> 
            Style["Unit Sphere:  \!\(\*OverscriptBox[\(r\), \
\(\[RightVector]\)]\)(u,v)={Cos[u] Sin[v], Sin[u] Sin[v], Cos[v]}", 15, Bold],
             PlotRange -> {{-1., 0.9999999999998993}, {-0.9999999999999748, 
             0.9999999999999748}, {-0.9999999999999748, 0.9999999999999748}}, 
            PlotRangePadding -> {
              Scaled[0.02], 
              Scaled[0.02], 
              Scaled[0.02]}}], $CellContext`Surf[
           Pattern[$CellContext`v, 
            Blank[]], 
           Pattern[$CellContext`w, 
            Blank[]]] := {
           $CellContext`X[1, $CellContext`v, $CellContext`w], 
           $CellContext`Y[1, $CellContext`v, $CellContext`w], 
           $CellContext`Z[
           1, $CellContext`v, $CellContext`w]}, $CellContext`Surf[
           Pattern[$CellContext`u, 
            Blank[]], 
           Pattern[$CellContext`v, 
            Blank[]], 
           Pattern[$CellContext`w, 
            Blank[]]] := {$CellContext`u (2 
            Cos[$CellContext`v]), $CellContext`u (2 
            Sin[$CellContext`v]), $CellContext`w (
            1 - $CellContext`u^2)}, $CellContext`X[
           Pattern[$CellContext`u, 
            Blank[]], 
           Pattern[$CellContext`v, 
            Blank[]], 
           Pattern[$CellContext`w, 
            Blank[]]] := $CellContext`u Cos[$CellContext`v] 
          Sin[$CellContext`w], $CellContext`Y[
           Pattern[$CellContext`u, 
            Blank[]], 
           Pattern[$CellContext`v, 
            Blank[]], 
           Pattern[$CellContext`w, 
            Blank[]]] := $CellContext`u Sin[$CellContext`v] 
          Sin[$CellContext`w], $CellContext`Z[
           Pattern[$CellContext`u, 
            Blank[]], 
           Pattern[$CellContext`v, 
            Blank[]], 
           Pattern[$CellContext`w, 
            Blank[]]] := $CellContext`u Cos[$CellContext`w], $CellContext`NR = 
         Graphics3D[{
            RGBColor[1, 0, 0], Arrowheads -> Small, 
            
            Arrow[{{0, -Sqrt[5/8 + Sqrt[5]/8], (-1 + Sqrt[5])/4}, {
              0, (-2) Sqrt[5/8 + Sqrt[5]/8], (-1 + Sqrt[5])/
               2}}]}], $CellContext`s$$ = (2 Pi)/5, $CellContext`Nr[
           Pattern[$CellContext`v, 
            Blank[]], 
           Pattern[$CellContext`w, 
            Blank[]]] = {
          Cos[$CellContext`v] Sin[$CellContext`w], Sin[$CellContext`v] 
           Sin[$CellContext`w], 
           Cos[$CellContext`w]}, $CellContext`Nr[
           Pattern[$CellContext`u, 
            Blank[]], 
           Pattern[$CellContext`v, 
            Blank[]], 
           Pattern[$CellContext`w, 
            Blank[]]] = {(4 $CellContext`u^2 $CellContext`w 
            Cos[$CellContext`v])/Sqrt[
           16 Abs[$CellContext`u^2 $CellContext`w Cos[$CellContext`v]]^2 + 
            16 Abs[$CellContext`u^2 $CellContext`w Sin[$CellContext`v]]^2 + 
            Abs[(-4) $CellContext`u Cos[$CellContext`v]^2 - 4 $CellContext`u 
               Sin[$CellContext`v]^2]^2], (4 $CellContext`u^2 $CellContext`w 
            Sin[$CellContext`v])/Sqrt[
           16 Abs[$CellContext`u^2 $CellContext`w Cos[$CellContext`v]]^2 + 
            16 Abs[$CellContext`u^2 $CellContext`w Sin[$CellContext`v]]^2 + 
            Abs[(-4) $CellContext`u Cos[$CellContext`v]^2 - 4 $CellContext`u 
               Sin[$CellContext`v]^2]^2], -(((-4) $CellContext`u 
              Cos[$CellContext`v]^2 - 4 $CellContext`u Sin[$CellContext`v]^2)/
            Sqrt[16 Abs[$CellContext`u^2 $CellContext`w 
                 Cos[$CellContext`v]]^2 + 
             16 Abs[$CellContext`u^2 $CellContext`w Sin[$CellContext`v]]^2 + 
             Abs[(-4) $CellContext`u Cos[$CellContext`v]^2 - 4 $CellContext`u 
                Sin[$CellContext`v]^2]^2])}, $CellContext`Fld = Graphics3D[{
            RGBColor[0, 0, 1], Arrowheads -> Small, 
            
            Arrow[{{0, -Sqrt[5/8 + Sqrt[5]/8], (-1 + Sqrt[5])/4}, {
              0, -1.4265847744427302`, 
               0.4635254915624212}}]}], $CellContext`F[{
            Pattern[$CellContext`x, 
             Blank[]], 
            Pattern[$CellContext`y, 
             Blank[]], 
            Pattern[$CellContext`z, 
             Blank[]]}, 
           Pattern[$CellContext`a, 
            Blank[]], 
           Pattern[$CellContext`b, 
            Blank[]], 
           Pattern[$CellContext`c, 
            
            Blank[]]] := {$CellContext`a $CellContext`x, $CellContext`b \
$CellContext`y, $CellContext`c $CellContext`z}, $CellContext`F[{
            Pattern[$CellContext`x, 
             Blank[]], 
            Pattern[$CellContext`y, 
             Blank[]], 
            Pattern[$CellContext`z, 
             
             Blank[]]}] := {$CellContext`z, $CellContext`x^2, \
$CellContext`y}, $CellContext`NrPlot = {
           Graphics3D[{
             RGBColor[1, 0, 0], Arrowheads -> Small, 
             
             Arrow[{{Sqrt[5/8 + Sqrt[5]/8] 
                Sin[Pi/20], ((-1 + Sqrt[5]) Sin[Pi/20])/4, 
                Cos[Pi/20]}, {
               2 Sqrt[5/8 + Sqrt[5]/8] 
                Sin[Pi/20], ((-1 + Sqrt[5]) Sin[Pi/20])/2, 2 Cos[Pi/20]}}]}], 
           Graphics3D[{
             RGBColor[1, 0, 0], Arrowheads -> Small, 
             
             Arrow[{{(Sqrt[5/8 + Sqrt[5]/8] (-1 + Sqrt[5]))/
                4, (-1 + Sqrt[5])^2/16, 
                Sqrt[
                5/8 + Sqrt[5]/8]}, {(Sqrt[5/8 + Sqrt[5]/8] (-1 + Sqrt[5]))/
                2, (-1 + Sqrt[5])^2/8, 2 Sqrt[5/8 + Sqrt[5]/8]}}]}], 
           Graphics3D[{
             RGBColor[1, 0, 0], Arrowheads -> Small, 
             
             Arrow[{{Sqrt[5/8 + Sqrt[5]/8] 
                Sin[(3 Pi)/20], ((-1 + Sqrt[5]) Sin[(3 Pi)/20])/4, 
                Cos[(3 Pi)/20]}, {
               2 Sqrt[5/8 + Sqrt[5]/8] 
                Sin[(3 Pi)/20], ((-1 + Sqrt[5]) Sin[(3 Pi)/20])/2, 2 
                Cos[(3 Pi)/20]}}]}], 
           Graphics3D[{
             RGBColor[1, 0, 0], Arrowheads -> Small, 
             Arrow[{{
                
                Sqrt[(5/8 - Sqrt[5]/8) (5/8 + Sqrt[5]/8)], (
                 Sqrt[5/8 - Sqrt[5]/8] (-1 + Sqrt[5]))/4, (1 + Sqrt[5])/4}, {
               2 Sqrt[(5/8 - Sqrt[5]/8) (5/8 + Sqrt[5]/8)], (
                 Sqrt[5/8 - Sqrt[5]/8] (-1 + Sqrt[5]))/2, (1 + Sqrt[5])/
                2}}]}], 
           Graphics3D[{
             RGBColor[1, 0, 0], Arrowheads -> Small, 
             Arrow[{{
                Sqrt[(5/8 + Sqrt[5]/8)/2], (-1 + Sqrt[5])/(4 Sqrt[2]), 1/Sqrt[
                2]}, {
                Sqrt[2 (5/8 + Sqrt[5]/8)], (-1 + Sqrt[5])/(2 Sqrt[2]), 
                Sqrt[2]}}]}], 
           Graphics3D[{
             RGBColor[1, 0, 0], Arrowheads -> Small, 
             
             Arrow[{{(Sqrt[5/8 + Sqrt[5]/8] (1 + Sqrt[5]))/
                4, ((-1 + Sqrt[5]) (1 + Sqrt[5]))/16, 
                Sqrt[
                5/8 - Sqrt[5]/8]}, {(Sqrt[5/8 + Sqrt[5]/8] (1 + Sqrt[5]))/
                2, ((-1 + Sqrt[5]) (1 + Sqrt[5]))/8, 2 
                Sqrt[5/8 - Sqrt[5]/8]}}]}], 
           Graphics3D[{
             RGBColor[1, 0, 0], Arrowheads -> Small, 
             
             Arrow[{{Sqrt[5/8 + Sqrt[5]/8] 
                Cos[(3 Pi)/20], ((-1 + Sqrt[5]) Cos[(3 Pi)/20])/4, 
                Sin[(3 Pi)/20]}, {
               2 Sqrt[5/8 + Sqrt[5]/8] 
                Cos[(3 Pi)/20], ((-1 + Sqrt[5]) Cos[(3 Pi)/20])/2, 2 
                Sin[(3 Pi)/20]}}]}], 
           Graphics3D[{
             RGBColor[1, 0, 0], Arrowheads -> Small, 
             
             Arrow[{{5/8 + Sqrt[5]/8, (Sqrt[5/8 + Sqrt[5]/8] (-1 + Sqrt[5]))/
                4, (-1 + Sqrt[5])/4}, {
               5/4 + Sqrt[5]/4, (Sqrt[5/8 + Sqrt[5]/8] (-1 + Sqrt[5]))/
                2, (-1 + Sqrt[5])/2}}]}], 
           Graphics3D[{
             RGBColor[1, 0, 0], Arrowheads -> Small, 
             
             Arrow[{{Sqrt[5/8 + Sqrt[5]/8] 
                Cos[Pi/20], ((-1 + Sqrt[5]) Cos[Pi/20])/4, 
                Sin[Pi/20]}, {
               2 Sqrt[5/8 + Sqrt[5]/8] 
                Cos[Pi/20], ((-1 + Sqrt[5]) Cos[Pi/20])/2, 2 Sin[Pi/20]}}]}], 
           Graphics3D[{
             RGBColor[1, 0, 0], Arrowheads -> Small, 
             Arrow[{{
                Sqrt[5/8 + Sqrt[5]/8], (-1 + Sqrt[5])/4, 0}, {
               2 Sqrt[5/8 + Sqrt[5]/8], (-1 + Sqrt[5])/2, 0}}]}], 
           Graphics3D[{
             RGBColor[1, 0, 0], Arrowheads -> Small, 
             
             Arrow[{{Sqrt[5/8 + Sqrt[5]/8] 
                Cos[Pi/20], ((-1 + Sqrt[5]) Cos[Pi/20])/4, -Sin[Pi/20]}, {
               2 Sqrt[5/8 + Sqrt[5]/8] 
                Cos[Pi/20], ((-1 + Sqrt[5]) Cos[Pi/20])/2, (-2) 
                Sin[Pi/20]}}]}], 
           Graphics3D[{
             RGBColor[1, 0, 0], Arrowheads -> Small, 
             
             Arrow[{{5/8 + Sqrt[5]/8, (Sqrt[5/8 + Sqrt[5]/8] (-1 + Sqrt[5]))/
                4, (1 - Sqrt[5])/4}, {
               5/4 + Sqrt[5]/4, (Sqrt[5/8 + Sqrt[5]/8] (-1 + Sqrt[5]))/
                2, (1 - Sqrt[5])/2}}]}], 
           Graphics3D[{
             RGBColor[1, 0, 0], Arrowheads -> Small, 
             
             Arrow[{{Sqrt[5/8 + Sqrt[5]/8] 
                Cos[(3 Pi)/20], ((-1 + Sqrt[5]) Cos[(3 Pi)/20])/4, -
                Sin[(3 Pi)/20]}, {
               2 Sqrt[5/8 + Sqrt[5]/8] 
                Cos[(3 Pi)/20], ((-1 + Sqrt[5]) Cos[(3 Pi)/20])/2, (-2) 
                Sin[(3 Pi)/20]}}]}], 
           Graphics3D[{
             RGBColor[1, 0, 0], Arrowheads -> Small, 
             
             Arrow[{{(Sqrt[5/8 + Sqrt[5]/8] (1 + Sqrt[5]))/
                4, ((-1 + Sqrt[5]) (1 + Sqrt[5]))/16, -
                Sqrt[5/8 - Sqrt[5]/8]}, {(
                 Sqrt[5/8 + Sqrt[5]/8] (1 + Sqrt[5]))/
                2, ((-1 + Sqrt[5]) (1 + Sqrt[5]))/8, (-2) 
                Sqrt[5/8 - Sqrt[5]/8]}}]}], 
           Graphics3D[{
             RGBColor[1, 0, 0], Arrowheads -> Small, 
             Arrow[{{
                Sqrt[(5/8 + Sqrt[5]/8)/2], (-1 + Sqrt[5])/(4 
                Sqrt[2]), -(1/Sqrt[2])}, {
                Sqrt[2 (5/8 + Sqrt[5]/8)], (-1 + Sqrt[5])/(2 Sqrt[2]), -
                Sqrt[2]}}]}], 
           Graphics3D[{
             RGBColor[1, 0, 0], Arrowheads -> Small, 
             Arrow[{{
                
                Sqrt[(5/8 - Sqrt[5]/8) (5/8 + Sqrt[5]/8)], (
                 Sqrt[5/8 - Sqrt[5]/8] (-1 + Sqrt[5]))/4, (-1 - Sqrt[5])/4}, {
               2 Sqrt[(5/8 - Sqrt[5]/8) (5/8 + Sqrt[5]/8)], (
                 Sqrt[5/8 - Sqrt[5]/8] (-1 + Sqrt[5]))/2, (-1 - Sqrt[5])/
                2}}]}], 
           Graphics3D[{
             RGBColor[1, 0, 0], Arrowheads -> Small, 
             
             Arrow[{{Sqrt[5/8 + Sqrt[5]/8] 
                Sin[(3 Pi)/20], ((-1 + Sqrt[5]) Sin[(3 Pi)/20])/4, -
                Cos[(3 Pi)/20]}, {
               2 Sqrt[5/8 + Sqrt[5]/8] 
                Sin[(3 Pi)/20], ((-1 + Sqrt[5]) Sin[(3 Pi)/20])/2, (-2) 
                Cos[(3 Pi)/20]}}]}], 
           Graphics3D[{
             RGBColor[1, 0, 0], Arrowheads -> Small, 
             
             Arrow[{{(Sqrt[5/8 + Sqrt[5]/8] (-1 + Sqrt[5]))/
                4, (-1 + Sqrt[5])^2/16, -
                Sqrt[5/8 + Sqrt[5]/8]}, {(
                 Sqrt[5/8 + Sqrt[5]/8] (-1 + Sqrt[5]))/2, (-1 + Sqrt[5])^2/
                8, (-2) Sqrt[5/8 + Sqrt[5]/8]}}]}], 
           Graphics3D[{
             RGBColor[1, 0, 0], Arrowheads -> Small, 
             
             Arrow[{{Sqrt[5/8 + Sqrt[5]/8] 
                Sin[Pi/20], ((-1 + Sqrt[5]) Sin[Pi/20])/4, -Cos[Pi/20]}, {
               2 Sqrt[5/8 + Sqrt[5]/8] 
                Sin[Pi/20], ((-1 + Sqrt[5]) Sin[Pi/20])/2, (-2) 
                Cos[Pi/20]}}]}], 
           Graphics3D[{
             RGBColor[1, 0, 0], Arrowheads -> Small, 
             Arrow[{{0, 0, -1}, {0, 0, -2}}]}], 
           Graphics3D[{
             RGBColor[1, 0, 0], Arrowheads -> Small, 
             
             Arrow[{{((1 + Sqrt[5]) Sin[Pi/20])/4, Sqrt[5/8 - Sqrt[5]/8] 
                Sin[Pi/20], 
                Cos[Pi/20]}, {((1 + Sqrt[5]) Sin[Pi/20])/2, 2 
                Sqrt[5/8 - Sqrt[5]/8] Sin[Pi/20], 2 Cos[Pi/20]}}]}], 
           Graphics3D[{
             RGBColor[1, 0, 0], Arrowheads -> Small, 
             
             Arrow[{{((-1 + Sqrt[5]) (1 + Sqrt[5]))/
                16, (Sqrt[5/8 - Sqrt[5]/8] (-1 + Sqrt[5]))/4, 
                Sqrt[5/8 + Sqrt[5]/8]}, {((-1 + Sqrt[5]) (1 + Sqrt[5]))/
                8, (Sqrt[5/8 - Sqrt[5]/8] (-1 + Sqrt[5]))/2, 2 
                Sqrt[5/8 + Sqrt[5]/8]}}]}], 
           Graphics3D[{
             RGBColor[1, 0, 0], Arrowheads -> Small, 
             
             Arrow[{{((1 + Sqrt[5]) Sin[(3 Pi)/20])/4, Sqrt[5/8 - Sqrt[5]/8] 
                Sin[(3 Pi)/20], 
                Cos[(3 Pi)/20]}, {((1 + Sqrt[5]) Sin[(3 Pi)/20])/2, 2 
                Sqrt[5/8 - Sqrt[5]/8] Sin[(3 Pi)/20], 2 Cos[(3 Pi)/20]}}]}], 
           Graphics3D[{
             RGBColor[1, 0, 0], Arrowheads -> Small, 
             
             Arrow[{{(Sqrt[5/8 - Sqrt[5]/8] (1 + Sqrt[5]))/4, 5/8 - Sqrt[5]/
                8, (1 + Sqrt[5])/4}, {(Sqrt[5/8 - Sqrt[5]/8] (1 + Sqrt[5]))/2,
                 5/4 - Sqrt[5]/4, (1 + Sqrt[5])/2}}]}], 
           Graphics3D[{
             RGBColor[1, 0, 0], Arrowheads -> Small, 
             Arrow[{{(1 + Sqrt[5])/(4 Sqrt[2]), 
                Sqrt[(5/8 - Sqrt[5]/8)/2], 1/Sqrt[2]}, {(1 + Sqrt[5])/(2 
                Sqrt[2]), 
                Sqrt[2 (5/8 - Sqrt[5]/8)], 
                Sqrt[2]}}]}], 
           Graphics3D[{
             RGBColor[1, 0, 0], Arrowheads -> Small, 
             
             Arrow[{{(1 + Sqrt[5])^2/
                16, (Sqrt[5/8 - Sqrt[5]/8] (1 + Sqrt[5]))/4, 
                Sqrt[5/8 - Sqrt[5]/8]}, {(1 + Sqrt[5])^2/
                8, (Sqrt[5/8 - Sqrt[5]/8] (1 + Sqrt[5]))/2, 2 
                Sqrt[5/8 - Sqrt[5]/8]}}]}], 
           Graphics3D[{
             RGBColor[1, 0, 0], Arrowheads -> Small, 
             Arrow[{{((1 + Sqrt[5]) Cos[(3 Pi)/20])/4, Sqrt[5/8 - Sqrt[5]/8] 
                Cos[(3 Pi)/20], 
                Sin[(3 Pi)/20]}, {((1 + Sqrt[5]) Cos[(3 Pi)/20])/2, 2 
                Sqrt[5/8 - Sqrt[5]/8] Cos[(3 Pi)/20], 2 Sin[(3 Pi)/20]}}]}], 
           Graphics3D[{
             RGBColor[1, 0, 0], Arrowheads -> Small, 
             Arrow[{{(Sqrt[5/8 + Sqrt[5]/8] (1 + Sqrt[5]))/4, 
                Sqrt[(5/8 - Sqrt[5]/8) (5/8 + Sqrt[5]/8)], (-1 + Sqrt[5])/
                4}, {(Sqrt[5/8 + Sqrt[5]/8] (1 + Sqrt[5]))/2, 2 
                Sqrt[(5/8 - Sqrt[5]/8) (5/8 + Sqrt[5]/8)], (-1 + Sqrt[5])/
                2}}]}], 
           Graphics3D[{
             RGBColor[1, 0, 0], Arrowheads -> Small, 
             
             Arrow[{{((1 + Sqrt[5]) Cos[Pi/20])/4, Sqrt[5/8 - Sqrt[5]/8] 
                Cos[Pi/20], 
                Sin[Pi/20]}, {((1 + Sqrt[5]) Cos[Pi/20])/2, 2 
                Sqrt[5/8 - Sqrt[5]/8] Cos[Pi/20], 2 Sin[Pi/20]}}]}], 
           Graphics3D[{
             RGBColor[1, 0, 0], Arrowheads -> Small, 
             Arrow[{{(1 + Sqrt[5])/4, 
                Sqrt[5/8 - Sqrt[5]/8], 0}, {(1 + Sqrt[5])/2, 2 
                Sqrt[5/8 - Sqrt[5]/8], 0}}]}], 
           Graphics3D[{
             RGBColor[1, 0, 0], Arrowheads -> Small, 
             
             Arrow[{{((1 + Sqrt[5]) Cos[Pi/20])/4, Sqrt[5/8 - Sqrt[5]/8] 
                Cos[Pi/20], -Sin[Pi/20]}, {((1 + Sqrt[5]) Cos[Pi/20])/2, 2 
                Sqrt[5/8 - Sqrt[5]/8] Cos[Pi/20], (-2) Sin[Pi/20]}}]}], 
           Graphics3D[{
             RGBColor[1, 0, 0], Arrowheads -> Small, 
             Arrow[{{(Sqrt[5/8 + Sqrt[5]/8] (1 + Sqrt[5]))/4, 
                Sqrt[(5/8 - Sqrt[5]/8) (5/8 + Sqrt[5]/8)], (1 - Sqrt[5])/
                4}, {(Sqrt[5/8 + Sqrt[5]/8] (1 + Sqrt[5]))/2, 2 
                Sqrt[(5/8 - Sqrt[5]/8) (5/8 + Sqrt[5]/8)], (1 - Sqrt[5])/
                2}}]}], 
           Graphics3D[{
             RGBColor[1, 0, 0], Arrowheads -> Small, 
             
             Arrow[{{((1 + Sqrt[5]) Cos[(3 Pi)/20])/4, Sqrt[5/8 - Sqrt[5]/8] 
                Cos[(3 Pi)/20], -
                Sin[(3 Pi)/20]}, {((1 + Sqrt[5]) Cos[(3 Pi)/20])/2, 2 
                Sqrt[5/8 - Sqrt[5]/8] Cos[(3 Pi)/20], (-2) 
                Sin[(3 Pi)/20]}}]}], 
           Graphics3D[{
             RGBColor[1, 0, 0], Arrowheads -> Small, 
             
             Arrow[{{(1 + Sqrt[5])^2/
                16, (Sqrt[5/8 - Sqrt[5]/8] (1 + Sqrt[5]))/4, -
                Sqrt[5/8 - Sqrt[5]/8]}, {(1 + Sqrt[5])^2/
                8, (Sqrt[5/8 - Sqrt[5]/8] (1 + Sqrt[5]))/2, (-2) 
                Sqrt[5/8 - Sqrt[5]/8]}}]}], 
           Graphics3D[{
             RGBColor[1, 0, 0], Arrowheads -> Small, 
             Arrow[{{(1 + Sqrt[5])/(4 Sqrt[2]), 
                Sqrt[(5/8 - Sqrt[5]/8)/2], -(1/Sqrt[2])}, {(1 + Sqrt[5])/(2 
                Sqrt[2]), 
                Sqrt[2 (5/8 - Sqrt[5]/8)], -Sqrt[2]}}]}], 
           Graphics3D[{
             RGBColor[1, 0, 0], Arrowheads -> Small, 
             
             Arrow[{{(Sqrt[5/8 - Sqrt[5]/8] (1 + Sqrt[5]))/4, 5/8 - Sqrt[5]/
                8, (-1 - Sqrt[5])/4}, {(Sqrt[5/8 - Sqrt[5]/8] (1 + Sqrt[5]))/
                2, 5/4 - Sqrt[5]/4, (-1 - Sqrt[5])/2}}]}], 
           Graphics3D[{
             RGBColor[1, 0, 0], Arrowheads -> Small, 
             
             Arrow[{{((1 + Sqrt[5]) Sin[(3 Pi)/20])/4, Sqrt[5/8 - Sqrt[5]/8] 
                Sin[(3 Pi)/20], -
                Cos[(3 Pi)/20]}, {((1 + Sqrt[5]) Sin[(3 Pi)/20])/2, 2 
                Sqrt[5/8 - Sqrt[5]/8] Sin[(3 Pi)/20], (-2) 
                Cos[(3 Pi)/20]}}]}], 
           Graphics3D[{
             RGBColor[1, 0, 0], Arrowheads -> Small, 
             
             Arrow[{{((-1 + Sqrt[5]) (1 + Sqrt[5]))/
                16, (Sqrt[5/8 - Sqrt[5]/8] (-1 + Sqrt[5]))/4, -
                Sqrt[5/8 + Sqrt[5]/8]}, {((-1 + Sqrt[5]) (1 + Sqrt[5]))/
                8, (Sqrt[5/8 - Sqrt[5]/8] (-1 + Sqrt[5]))/2, (-2) 
                Sqrt[5/8 + Sqrt[5]/8]}}]}], 
           Graphics3D[{
             RGBColor[1, 0, 0], Arrowheads -> Small, 
             
             Arrow[{{((1 + Sqrt[5]) Sin[Pi/20])/4, Sqrt[5/8 - Sqrt[5]/8] 
                Sin[Pi/20], -Cos[Pi/20]}, {((1 + Sqrt[5]) Sin[Pi/20])/2, 2 
                Sqrt[5/8 - Sqrt[5]/8] Sin[Pi/20], (-2) Cos[Pi/20]}}]}], 
           Graphics3D[{
             RGBColor[1, 0, 0], Arrowheads -> Small, 
             Arrow[{{0, 0, -1}, {0, 0, -2}}]}], 
           Graphics3D[{
             RGBColor[1, 0, 0], Arrowheads -> Small, 
             
             Arrow[{{Sqrt[5/8 - Sqrt[5]/8] 
                Sin[Pi/20], ((1 + Sqrt[5]) Sin[Pi/20])/4, 
                Cos[Pi/20]}, {
               2 Sqrt[5/8 - Sqrt[5]/8] Sin[Pi/20], ((1 + Sqrt[5]) Sin[Pi/20])/
                2, 2 Cos[Pi/20]}}]}], 
           Graphics3D[{
             RGBColor[1, 0, 0], Arrowheads -> Small, 
             
             Arrow[{{(Sqrt[5/8 - Sqrt[5]/8] (-1 + Sqrt[5]))/
                4, ((-1 + Sqrt[5]) (1 + Sqrt[5]))/16, 
                Sqrt[
                5/8 + Sqrt[5]/8]}, {(Sqrt[5/8 - Sqrt[5]/8] (-1 + Sqrt[5]))/
                2, ((-1 + Sqrt[5]) (1 + Sqrt[5]))/8, 2 
                Sqrt[5/8 + Sqrt[5]/8]}}]}], 
           Graphics3D[{
             RGBColor[1, 0, 0], Arrowheads -> Small, 
             
             Arrow[{{Sqrt[5/8 - Sqrt[5]/8] 
                Sin[(3 Pi)/20], ((1 + Sqrt[5]) Sin[(3 Pi)/20])/4, 
                Cos[(3 Pi)/20]}, {
               2 Sqrt[5/8 - Sqrt[5]/8] 
                Sin[(3 Pi)/20], ((1 + Sqrt[5]) Sin[(3 Pi)/20])/2, 2 
                Cos[(3 Pi)/20]}}]}], 
           Graphics3D[{
             RGBColor[1, 0, 0], Arrowheads -> Small, 
             
             Arrow[{{5/8 - Sqrt[5]/8, (Sqrt[5/8 - Sqrt[5]/8] (1 + Sqrt[5]))/
                4, (1 + Sqrt[5])/4}, {
               5/4 - Sqrt[5]/4, (Sqrt[5/8 - Sqrt[5]/8] (1 + Sqrt[5]))/
                2, (1 + Sqrt[5])/2}}]}], 
           Graphics3D[{
             RGBColor[1, 0, 0], Arrowheads -> Small, 
             Arrow[{{
                Sqrt[(5/8 - Sqrt[5]/8)/2], (1 + Sqrt[5])/(4 Sqrt[2]), 1/Sqrt[
                2]}, {
                Sqrt[2 (5/8 - Sqrt[5]/8)], (1 + Sqrt[5])/(2 Sqrt[2]), 
                Sqrt[2]}}]}], 
           Graphics3D[{
             RGBColor[1, 0, 0], Arrowheads -> Small, 
             
             Arrow[{{(Sqrt[5/8 - Sqrt[5]/8] (1 + Sqrt[5]))/4, (1 + Sqrt[5])^2/
                16, 
                Sqrt[
                5/8 - Sqrt[5]/8]}, {(Sqrt[5/8 - Sqrt[5]/8] (1 + Sqrt[5]))/
                2, (1 + Sqrt[5])^2/8, 2 Sqrt[5/8 - Sqrt[5]/8]}}]}], 
           Graphics3D[{
             RGBColor[1, 0, 0], Arrowheads -> Small, 
             Arrow[{{
               Sqrt[5/8 - Sqrt[5]/8] 
                Cos[(3 Pi)/20], ((1 + Sqrt[5]) Cos[(3 Pi)/20])/4, 
                Sin[(3 Pi)/20]}, {
               2 Sqrt[5/8 - Sqrt[5]/8] 
                Cos[(3 Pi)/20], ((1 + Sqrt[5]) Cos[(3 Pi)/20])/2, 2 
                Sin[(3 Pi)/20]}}]}], 
           Graphics3D[{
             RGBColor[1, 0, 0], Arrowheads -> Small, 
             Arrow[{{
                
                Sqrt[(5/8 - Sqrt[5]/8) (5/8 + Sqrt[5]/8)], (
                 Sqrt[5/8 + Sqrt[5]/8] (1 + Sqrt[5]))/4, (-1 + Sqrt[5])/4}, {
               2 Sqrt[(5/8 - Sqrt[5]/8) (5/8 + Sqrt[5]/8)], (
                 Sqrt[5/8 + Sqrt[5]/8] (1 + Sqrt[5]))/2, (-1 + Sqrt[5])/
                2}}]}], 
           Graphics3D[{
             RGBColor[1, 0, 0], Arrowheads -> Small, 
             
             Arrow[{{Sqrt[5/8 - Sqrt[5]/8] 
                Cos[Pi/20], ((1 + Sqrt[5]) Cos[Pi/20])/4, 
                Sin[Pi/20]}, {
               2 Sqrt[5/8 - Sqrt[5]/8] Cos[Pi/20], ((1 + Sqrt[5]) Cos[Pi/20])/
                2, 2 Sin[Pi/20]}}]}], 
           Graphics3D[{
             RGBColor[1, 0, 0], Arrowheads -> Small, 
             Arrow[{{
                Sqrt[5/8 - Sqrt[5]/8], (1 + Sqrt[5])/4, 0}, {
               2 Sqrt[5/8 - Sqrt[5]/8], (1 + Sqrt[5])/2, 0}}]}], 
           Graphics3D[{
             RGBColor[1, 0, 0], Arrowheads -> Small, 
             
             Arrow[{{Sqrt[5/8 - Sqrt[5]/8] 
                Cos[Pi/20], ((1 + Sqrt[5]) Cos[Pi/20])/4, -Sin[Pi/20]}, {
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             Arrow[{{((-1 + Sqrt[5]) Sin[(3 Pi)/20])/4, Sqrt[5/8 + Sqrt[5]/8] 
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             Arrow[{{((1 - Sqrt[5]) Cos[(3 Pi)/20])/4, Sqrt[5/8 + Sqrt[5]/8] 
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             Arrow[{{((1 - Sqrt[5]) Sin[(3 Pi)/20])/4, Sqrt[5/8 + Sqrt[5]/8] 
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