(************** Content-type: application/mathematica ************** CreatedBy='Mathematica 4.2' Mathematica-Compatible Notebook This notebook can be used with any Mathematica-compatible application, such as Mathematica, MathReader or Publicon. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). NOTE: If you modify the data for this notebook not in a Mathematica- compatible application, you must delete the line below containing the word CacheID, otherwise Mathematica-compatible applications may try to use invalid cache data. For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. *******************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 119624, 1959]*) (*NotebookOutlinePosition[ 120353, 1984]*) (* CellTagsIndexPosition[ 120309, 1980]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell["Autocad LT and the Coxeter Graph", "Title"], Cell[CellGroupData[{ Cell["Author", "Subsection"], Cell["\<\ Ed Pegg Jr. Wolfram Research, Inc. April 8, 2003\ \>", "Text"], Cell[CellGroupData[{ Cell["Implementation", "Subsubsection"], Cell[TextData[{ "Turning an Autocad object into a ", StyleBox["Mathematica", FontSlant->"Italic"], " object requires a small amount of effort. The easiest way is to save \ Autocad line art as DXF, Import as DXF into ", StyleBox["Mathematica", FontSlant->"Italic"], ", and then to strip the zeroes. For this demonstration, I made a nice \ embedding of the Coxeter Graph. More information on this object can be seen \ at ", ButtonBox["http://mathworld.wolfram.com/CoxeterGraph.html", ButtonData:>{ URL[ "http://mathworld.wolfram.com/CoxeterGraph.html"], None}, ButtonStyle->"Hyperlink"], ". " }], "Text"], Cell[BoxData[ \(\(coxeter\ = \ Import["\", "\"];\)\)], "Input"], Cell["\<\ There are two equivalent ways of converting the 3D DXF file into a 2D object, \ both involving stripping the zeroes. 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The Graphs package is by Eric \ Weisstein, and can be found at ", ButtonBox["http://library.wolfram.com/infocenter/MathSource/4775/", ButtonData:>{ URL[ "http://library.wolfram.com/infocenter/MathSource/4775/"], None}, ButtonStyle->"Hyperlink"], " or ", ButtonBox["http://mathworld.wolfram.com/packages/", ButtonData:>{ URL[ "http://mathworld.wolfram.com/packages/"], None}, ButtonStyle->"Hyperlink"], "." }], "Text"], Cell[BoxData[{ \(\(<< DiscreteMath`Combinatorica`;\)\), "\[IndentingNewLine]", \(\(<< Graphs`;\)\)}], "Input"], Cell["\<\ After loading the packages, the line object can be converted into a \ Combinatorica object. The .1 at the end cleans up some vertices that are \ incorrectly separated. If removed, the graph will have too many vertices.\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(temp\ = LinesToGraph[ Graphics[ Map[Drop[#, \(-1\)] &, Map[Last, First[coxeter]], {\(-2\)}]], .1]\)], "Input"], Cell[BoxData[ InterpretationBox[\("\[SkeletonIndicator]Graph:<"\[InvisibleSpace]42\ \[InvisibleSpace]", "\[InvisibleSpace]28\[InvisibleSpace]", \ "\[InvisibleSpace]"Undirected"\[InvisibleSpace]">\[SkeletonIndicator]"\), SequenceForm[ "\[SkeletonIndicator]Graph:<", 42, ", ", 28, ", ", "Undirected", ">\[SkeletonIndicator]"], Editable->False]], "Output"] }, Open ]], Cell["\<\ The way Combinatorica programming is set up, in an undirected graph, the \ lines must always be set up as {{lesser, greater}}. 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