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For manual installation copy the code from the bottom of this post and save it as "PolygonPlotMarkers.m" in the directory SystemOpen[FileNameJoin[{$UserBaseDirectory, "Applications"}]].

For manual installation copy the code from GitHub, and save it as "PolygonPlotMarkers.m" in the directory SystemOpen[FileNameJoin[{$UserBaseDirectory, "Applications"}]].

The GitHib version and this post are updated, the update for WFR version is submitted, will be published soon. The package code has now been removed from this post due to exceeding the 30,000 character limit per post.

The GitHib version, the WFR version and this post are updated. The package code has now been removed from this post due to exceeding the 30,000 character limit per post.

The GitHub version and this post will be updated soon.

• The basic usage syntax is PolygonMarker[shape, size] where shape is a name of built-in shape or a list of 2D coordinates describing a non-selfintersecting polygon. The size can be given as a number or in Scaled or Offset form.

• PolygonMarker[All] and PolygonMarker[] return the list of names of built-in shapes.

• PolygonMarker[shape, size] returns Polygon graphics primitive which can be used in Graphics.

• PolygonMarker[shape, size, style], where style is a list of graphics directives applied to shape, returns a Graphics object which can be used as a marker for PlotMarkers.

• PolygonMarker[shape, size, style, options] returns a Graphics object with options applied.

• With Offset size specification the plot marker has fixed size specified in printer's points independent of the size of the plot.

• PolygonMarkers with identical size specifications have equal areas (not counting the area taken by the edge of generated Polygon). PolygonMarker[shape, size] returns shape with area size2 in the internal coordinate system of Graphics. PolygonMarker[shape, Offset[size]] returns shape with area size2 square printer's points.

• The centroid of polygon returned by PolygonMarker[shape, size] is always placed at {0, 0} in the internal coordinate system of Graphics.

• PolygonMarker[shape, size, positions] where positions is a list of 2D coordinates evaluates to Translate[PolygonMarker[shape, size], positions]. It represents a collection of multiple identical copies of the shape with centroids placed at positions.

{"TripleCross", "Y", "UpTriangle", "UpTriangleTruncated", "DownTriangle", 
 "DownTriangleTruncated", "LeftTriangle", "LeftTriangleTruncated", "RightTriangle", 
 "RightTriangleTruncated", "ThreePointedStar", "Cross", "DiagonalCross", "Diamond", 
 "Square", "FourPointedStar", "DiagonalFourPointedStar", "FivefoldCross", "Pentagon", 
 "FivePointedStar", "FivePointedStarThick", "SixfoldCross", "Hexagon", "SixPointedStar", 
 "SixPointedStarSlim", "SevenfoldCross", "SevenPointedStar", "SevenPointedStarNeat", 
 "SevenPointedStarSlim", "EightfoldCross", "Disk", "H", "I", "N", "Z", "S", "Sw", "Sl"}

The code of the package

BeginPackage["PolygonPlotMarkers`"];

ClearAll[PolygonMarker];
PolygonMarker::usage="\!\(\*RowBox[{\"PolygonMarker\", \"[\",StyleBox[\"\\\"\\!\\(\\*StyleBox[\\\"name\\\",\\\"TI\\\"]\\)\\\"\", ShowStringCharacters->True], \"]\"}]\) returns a unit area Polygon describing the shape \!\(\*StyleBox[\"\\\"\\!\\(\\*StyleBox[\\\"name\\\",\\\"TI\\\"]\\)\\\"\", ShowStringCharacters->True]\) with centroid at {0,0}.\n\!\(\*RowBox[{\"PolygonMarker\", \"[\", RowBox[{\"{\", RowBox[{SubscriptBox[StyleBox[\"p\", \"TI\"], StyleBox[\"1\", \"TR\"]], \",\", \ StyleBox[\"\[Ellipsis]\", \"TR\"], \",\", SubscriptBox[StyleBox[\"p\", \"TI\"], StyleBox[\"n\", \"TI\"]]}], \"}\"}], \"]\"}]\) returns a unit area Polygon with shape described by points \!\(\*SubscriptBox[StyleBox[\"p\", \"TI\"], StyleBox[\"i\", \"TI\"]]\) and centroid at {0,0}.\n\!\(\*RowBox[{\"PolygonMarker\", \"[\", RowBox[{StyleBox[\"shape\", \"TI\"], \",\", StyleBox[\"size\", \"TI\"]}], \"]\"}]\) returns Polygon of \!\(\*StyleBox[\"shape\", \"TI\"]\) with centroid at {0,0} and area \!\(\*SuperscriptBox[StyleBox[\"size\", \"TI\"], StyleBox[\"2\", \"TR\"]]\).\n\!\(\*RowBox[{\"PolygonMarker\", \"[\", RowBox[{StyleBox[\"shape\", \"TI\"], \",\", StyleBox[\"size\", \"TI\"], \",\", StyleBox[\"style\", \"TI\"]}], \"]\"}]\) returns a Graphics object which can be used as a marker for PlotMarkers where the style of \!\(\*StyleBox[\"shape\", \"TI\"]\) is defined by \!\(\*StyleBox[\"style\", \"TI\"]\).\n\!\(\*RowBox[{\"PolygonMarker\", \"[\",\"All\", \"]\"}]\) returns the list of names of predefined shapes.";
SyntaxInformation[PolygonMarker]={"ArgumentsPattern"->{_,_.,_.,OptionsPattern[]}};
PolygonMarker::nonsimple="The specified shape doesn't represent a simple polygon.";
Options[PolygonMarker] = {AlignmentPoint -> {0,0}, BaselinePosition -> Axis, AspectRatio -> Automatic, Axes -> False, AxesLabel -> None, AxesOrigin -> {0,0}, AxesStyle -> {}, Background -> None, BaseStyle -> {},  ContentSelectable -> Automatic, CoordinatesToolOptions -> Automatic, DisplayFunction :> Identity, Epilog -> {}, FormatType :> TraditionalForm, Frame -> False, FrameLabel -> None, FrameStyle -> {}, FrameTicks -> Automatic, FrameTicksStyle -> {}, GridLines -> None, GridLinesStyle -> {}, ImageMargins -> 0., ImagePadding -> All, ImageSize -> Automatic, ImageSizeRaw -> Automatic, LabelStyle -> {}, Method -> Automatic, PlotLabel -> None, PlotRange -> All, PlotRangeClipping -> False, PlotRangePadding -> Automatic, PlotRegion -> Automatic, PreserveImageOptions -> Automatic, Prolog -> {}, RotateLabel -> True, Ticks -> Automatic, TicksStyle -> {}};

Begin["`Private`"];

ClearAll[PolygonArea,PolygonCentroid,LineIntersectionPoint,ngon,nstar,ncross,scale,coords];
(*The shoelace method for computing the area of polygon http://mathematica.stackexchange.com/a/22587/280*)
PolygonArea[pts_?MatrixQ]:=Abs@Total[Det/@Partition[pts,2,1,1]]/2;
(*http://mathematica.stackexchange.com/a/7715/280*)
PolygonCentroid[pts_?MatrixQ]:=With[{dif=Map[Det,Partition[pts,2,1,{1,1}]]},ListConvolve[{{1,1}},Transpose[pts],{-1,-1}] . dif/(3 Total[dif])];
(*http://mathematica.stackexchange.com/a/51399/280*)
LineIntersectionPoint[{a_,b_},{c_,d_}]:=(Det[{a,b}] (c-d)-Det[{c,d}] (a-b))/Det[{a-b,c-d}];

ngon[n_,phase_:0]:=Table[{0,1} . RotationMatrix[2k Pi/n+phase],{k,0,n-1}];
(* 
   nn - number of vertices in related polygram
   step - step at which vertices in the polygram are connected (must be lesser than nn/2)
   n - number of points in the final star (must be divisor of nn)  an illustration: http://en.wikipedia.org/wiki/Star_polygon#Simple_isotoxal_star_polygons
*)

nstar[n_/;n>=5,phase_:0]:=nstar[n,2,n,phase];
nstar[nn_,step_,n_,phase_:0]/;Divisible[nn,n]&&nn/2>step>nn/n:=Module[{a1,a2,b1,b2,ab},{a1,a2,b1,b2}=ngon[nn][[{1,1+step,1+nn/n,nn/n-step}]];
ab=LineIntersectionPoint[{a1,a2},{b1,b2}];
Flatten[Table[{a1,ab} . RotationMatrix[2k Pi/n+phase],{k,0,n-1}],1]];
(*a-semiwidths of the crossing stripes*)
ncross[n_,phase_:0,a_:1/10]:=Flatten[NestList[# . RotationMatrix[2Pi/n]&,{{-a,1},{a,1},{a,a Cot[Pi/n]}} . RotationMatrix[phase],n-1],1];

(*Unitizes the area of the polygon*)
scale[coords_]:=Chop[#/Sqrt@PolygonArea@#]&@N[coords,{18,18}];

coords["UpTriangle"|"Triangle"]=ngon[3]//scale;
coords["DownTriangle"]=ngon[3,Pi/3]//scale;
coords["LeftTriangle"]=ngon[3,Pi/6]//scale;
coords["RightTriangle"]=ngon[3,-Pi/6]//scale;
coords["ThreePointedStar"]=nstar[12,5,3]//scale;
coords["DiagonalSquare"|"Diamond"]=ngon[4,0]//scale;
coords["Square"]=ngon[4,Pi/4]//scale;
coords["FourPointedStar"]=nstar[8,3,4]//scale;
coords["DiagonalFourPointedStar"]=nstar[8,3,4,Pi/4]//scale;
coords["Pentagon"]=ngon[5]//scale;
coords["FivePointedStar"]=nstar[5]//scale;
coords["FivePointedStarThick"]=nstar[20,7,5]//scale;
coords["Hexagon"]=ngon[6]//scale;
coords["SixPointedStar"]=nstar[6]//scale;
coords["SixPointedStarSlim"]=nstar[12,5,6]//scale;
coords["SevenPointedStar"]=nstar[7]//scale;
coords["SevenPointedStarNeat"]=nstar[14,5,7]//scale;
coords["SevenPointedStarSlim"]=nstar[14,6,7]//scale;
coords["Cross"|"+"]=ncross[4]//scale;
coords["DiagonalCross"|"CrossDiagonal"|"X"|"x"]=ncross[4,Pi/4]//scale;
coords["TripleCross"|"TripleCrossUp"]=ncross[3]//scale;
coords["TripleCrossDown"|"Y"|"y"]=ncross[3,Pi/3]//scale;
coords["FivefoldCross"]=ncross[5]//scale;
coords["SixfoldCross"]=ncross[6]//scale;
coords["SevenfoldCross"]=ncross[7]//scale;
coords["EightfoldCross"]=ncross[8]//scale;
(*The truncated triangle shape originates from the Cross's Theorem http://demonstrations.wolfram.com/CrosssTheorem/*)
coords["UpTriangleTruncated"|"TriangleTruncated"|"TruncatedTriangle"]=Flatten[{{-3,6+Sqrt[3]},{3,6+Sqrt[3]}} . RotationMatrix[# Pi/3]&/@{0,2,4},1]//scale;
coords["DownTriangleTruncated"]=coords["UpTriangleTruncated"] . ReflectionMatrix[{0,1}];
coords["LeftTriangleTruncated"]=coords["UpTriangleTruncated"] . RotationMatrix[Pi/6];
coords["RightTriangleTruncated"]=coords["UpTriangleTruncated"] . RotationMatrix[-Pi/6];
(*Disk approximated by 24-gon*)
coords["Disk"|"Circle"]=ngon[24]//scale;

(*Plotting symbols recommended in[Cleveland W.S.The Elements of Graphing Data (1985)]*)
(*Symmetric symbol "H"*)
coords["H"]=Join[#,-#]&@Join[#,Reverse@# . {{1,0},{0,-1}}]&@{{333,108},{333,630},{585,630}}//scale;
(*Symmetric symbol "I"*)
coords["I"]=Join[#,-#]&@{{-20,-68},{-64,-68},{-64,-104},{64,-104},{64,-68},{20,-68}}//scale;
(*Antisymmetric symbol "N"*)
coords["N"]=Join[#,-#]&@{{18,-32},{30,-32},{30,32},{17,32},{17,-12}}//scale;
(*Antisymmetric symbol "Z"*)
coords["Z"]=Join[#,-#]&@{{-567,-432},{-567,-630},{567,-630},{567,-414},{-234,-414}}//scale;
(*Antisymmetric symbol "S" (simple)*)
coords["S"]=Join[#,-#]&@{{-176,-54},{116,-54},{167,-100},{167,-170},{116,-216},{-284,-216},{-284,-324},{176,-324},{293,-216},{293,-54}}//scale;
(*Antisymmetric symbol "S" (curved,long)*)
coords["LongS"|"SLong"|"Sl"]=Join[#,-#]&@{{-(49/16),-(3/11)},{-(425/91),23/28},{-(141/26),31/12},{-(165/32),88/19},{-(167/45),106/17},{-(24/17),149/21},{121/69,233/33},{130/27,31/5},{130/27,118/29},{127/47,199/39},{7/20,233/42},{-(12/7),139/26},{-(65/21),139/31},{-(395/113),114/35},{-(157/52),77/39},{-(83/44),56/41},{9/22,39/43}}//scale;
(*Antisymmetric symbol "S" (curved,wide)*)
coords["WideS"|"SWide"|"Sw"]=Join[#,-#]&@{{80/11,-(3/5)},{49/6,-(9/4)},{97/12,-(41/11)},{39/5,-(35/8)},{88/13,-(65/12)},{51/10,-(49/8)},{2,-(13/2)},{-(20/11),-(13/2)},{-(37/8),-(81/13)},{-(81/13),-(40/7)},{-(59/8),-(54/11)},{-(81/10),-(26/7)},{-(70/11),-(29/9)},{-(57/11),-(46/11)},{-(11/4),-(33/7)},{11/7,-(19/4)},{16/3,-(37/9)},{31/5,-(38/11)},{32/5,-(38/13)},{37/6,-(49/24)},{61/13,-(6/5)},{23/7,-(13/14)},{-(25/9),-(4/5)},{-(23/4),-(3/13)}}//scale;

PolygonMarker[name_String]:=Polygon[coords[name]];
PolygonMarker[name_String,size_?NumericQ]:=Polygon[size coords[name]];
PolygonMarker[name_String,(h:Scaled|Offset)[size_?NumericQ]]:=Polygon[h[size #,{0,0}]&/@coords[name]];
PolygonMarker[coords:{{_?NumericQ,_?NumericQ}..},size_?NumericQ]:=Polygon[size N[scale[Transpose[Transpose[coords]-PolygonCentroid[coords]]],{16,16}]];
PolygonMarker[coords:{{_?NumericQ,_?NumericQ}..},Scaled[size_?NumericQ]]:=Polygon[Scaled[size #,{0,0}]&/@N[scale[Transpose[Transpose[coords]-PolygonCentroid[coords]]],{16,16}]];
PolygonMarker[arg:_String|{{_?NumericQ,_?NumericQ}..},size:_?NumericQ|(Scaled|Offset)[_?NumericQ],positions:{_?NumericQ,_?NumericQ}|{{_?NumericQ,_?NumericQ}..}]:=Translate[PolygonMarker[arg,size],positions];
PolygonMarker[]=PolygonMarker[All]={"TripleCross","Y","UpTriangle","UpTriangleTruncated","DownTriangle","DownTriangleTruncated","LeftTriangle","LeftTriangleTruncated","RightTriangle","RightTriangleTruncated","ThreePointedStar","Cross","DiagonalCross","Diamond","Square","FourPointedStar","DiagonalFourPointedStar","FivefoldCross","Pentagon","FivePointedStar","FivePointedStarThick","SixfoldCross","Hexagon","SixPointedStar","SixPointedStarSlim","SevenfoldCross","SevenPointedStar","SevenPointedStarNeat","SevenPointedStarSlim","EightfoldCross","Disk","H","I","N","Z","S","Sw","Sl"};
(*A subset of plot markers suitable for use when plotting symbols on the plot significantly overlap.*)
PolygonMarker["Overlap"]={"TripleCross","Y","UpTriangle","DownTriangle","LeftTriangle","RightTriangle","ThreePointedStar","Cross","DiagonalCross","Diamond","Square","FourPointedStar","DiagonalFourPointedStar","FivefoldCross","FivePointedStar","FivePointedStarThick","Disk","H","I","N","Z","S","Sw","Sl"};
(* Generate a Graphics object which can be used as a marker for PlotMarkers *)
PolygonMarker[shape_,size_,g_]:=PolygonMarker[shape,size,{g}];
PolygonMarker[shape_,size_,{g___}]:=Block[{p=PolygonMarker[shape,size]},Graphics[{g,p},AlignmentPoint->{0,0},ImagePadding->All,PlotRange->All]/;Head[p]===Polygon];
(* This form allows to construct composite plot markers containing additional graphics primitives *)
PolygonMarker[shape_,size_,{{g___},{primitives___}}]:=Block[{p=PolygonMarker[shape,size]},Graphics[{{g,p},{primitives}},AlignmentPoint->{0,0},ImagePadding->All,PlotRange->All]/;Head[p]===Polygon];
(* This form allows to pass any Graphics options as an argument of PolygonMarker *)
PolygonMarker[shape_,size_,style_,opts:OptionsPattern[]]:=Block[{gr=PolygonMarker[shape,size,style]},Show[gr,opts]/;Head[gr]===Graphics];

End[];

EndPackage[];

UPDATE from July 2022

A minor update: now the form PolygonMarker[shape, spec, positions], where spec contains numeric specification for size, returns a list of Polygon graphics primitives with centroids placed at positions (instead of a Translate object, as it was earlier). This change makes straightforward producing explicit primitives intended for the Region-based functionality. As always, this version has no incompatible changes.

Added fouth example under the "Scope" section on the Documentation page for PolygonMarker, which uses the Region-based functionality for producing a high-quality vector figure. This example is also published in this post.

The GitHib version and this post are updated, the update for WFR version is submitted, will be published soon. The package code has now been removed from this post due to exceeding the 30,000 character limit per post.

• The basic usage syntax is PolygonMarker[shape, spec] where shape is a name of built-in shape or a list of 2D coordinates describing a non-selfintersecting polygon, and spec can be either size or {size, angle}. 

• The size can be given as a number or in Scaled or Offset form.

• The angle in radians determines the angle of counterclocwise rotation of shape about its centroid.

• PolygonMarker[All] and PolygonMarker[] return the list of names of built-in shapes.

• PolygonMarker[shape, spec] returns Polygon graphics primitive which can be used in Graphics.

• PolygonMarker[shape, size, style], where style is a list of graphics directives applied to shape, returns a Graphics object which can be used as a marker for PlotMarkers.

• PolygonMarker[shape, size, style, options] returns a Graphics object with options applied.

• With Offset size specification the plot marker has fixed size specified in printer's points independent of the size of the plot.

• PolygonMarkers with identical size specifications have equal areas (not counting the area taken by the edge of generated Polygon). PolygonMarker[shape, size] returns shape with area size2 in the internal coordinate system of Graphics. PolygonMarker[shape, Offset[size]] returns shape with area size2 square printer's points.

• The centroid of polygon returned by PolygonMarker[shape, size] is always placed at {0, 0} in the internal coordinate system of Graphics.

• PolygonMarker[shape, spec, positions] where positions is a list of 2D coordinates evaluates and spec contains numeric specification for size, returns a list of Polygon graphics primitives with centroids placed at positions.

• PolygonMarker[shape, spec, positions] where positions is a list of 2D coordinates and spec contains Scaled or Offset specification for size, evaluates to Translate[PolygonMarker[shape, size], positions]. It represents a collection of multiple identical copies of the shape with centroids placed at positions.

{"TripleCross", "Y", "UpTriangle", "UpTriangleTruncated",  
"DownTriangle", "DownTriangleTruncated", "LeftTriangle",  
"LeftTriangleTruncated", "RightTriangle", "RightTriangleTruncated",  
"ThreePointedStar", "Cross", "DiagonalCross", "Diamond", "Square",  
"FourPointedStar", "DiagonalFourPointedStar", "FivefoldCross",  
"Pentagon", "FivePointedStar", "FivePointedStarSlim",  
"FivePointedStarThick", "DancingStar", "DancingStarRight", 
"DancingStarThick", "DancingStarThickRight", "SixfoldCross",  
"Hexagon", "SixPointedStar", "SixPointedStarSlim", "SixfoldPinwheel", 
"SixfoldPinwheelRight", "SevenfoldCross", "SevenPointedStar", 
"SevenPointedStarNeat", "SevenPointedStarSlim", "SevenfoldPinwheel", 
"SevenfoldPinwheelRight", "EightfoldCross", "Disk", "H", "I", "N",  
"Z", "S", "Sw", "Sl"}