File:Dodecahedron S-realization map.svg

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Description
English: Symmetric realizations of the dodecahedron (or its Petrial). Crossed nodes indicate a non-faithful realization. Edges represent blending by a pure realization. Parallel edges, or edges of the same color/style correspond to blends by the same polyhedron. This is the Hasse diagram on the lattice formed with blending as the meet.
Date 21:02, 28 December 2023 (UTC)
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Source code
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LaTeX code

\documentclass{standalone}

\usepackage{tikz}
\usetikzlibrary{decorations.pathmorphing,calc}
\newcommand\ax{-8}
\newcommand\bx{-3}
\newcommand\cx{2}
\newcommand\dx{3}
\newcommand\ex{6}

\newcommand\ay{3}
\newcommand\by{3}
\newcommand\cy{4}
\newcommand\dy{4}
\newcommand\ey{5}

\NewDocumentCommand\blend{md()}{
  \draw[l#2]($#1$)--($#1+(#2)$)
}
\begin{document}
\begin{tikzpicture}
  [ every node/.style={outer sep=0pt,thick,minimum size=.1,circle,draw=black,fill=white,solid}
  , cross/.style=
      { draw=none
      , fill=none
      , path picture={
        \draw[black](path picture bounding box.south west)--(path picture bounding box.north east);
        \draw[black](path picture bounding box.south east)--(path picture bounding box.north west);
      }
    }
  , lA/.style={thick, blue}
  , lB/.style={thick, green, dashed}
  , lC/.style={thick, red, double}
  , lD/.style={thick, yellow, decorate, decoration=snake}
  , lE/.style={thick, magenta, dash dot}
  ]
  \coordinate (Z) at (0,0);
  \coordinate (A) at (\ax,\ay);
  \coordinate (B) at (\bx,\by);
  \coordinate (C) at (\cx,\cy);
  \coordinate (D) at (\dx,\dy);
  \coordinate (E) at (\ex,\ey);
  \foreach \dim in {0,3,4,5,6,7,8,9,10,11,12,13,14,15,16,19}{
    \draw[semithick, dashed](\ax+\bx-1,\dim)node[draw=none,fill=none,left]{\dim}--(\cx+\dx+\ex+1,\dim);
  }
  \node[left,fill=none,draw=none]()at(\ax+\bx-1,20){Dim:};
  \foreach \bOn in {Z,B}{
    \foreach \cOn in {Z,C}{
      \foreach \dOn in {Z,D}{
        \foreach \eOn in {Z,E}{
          \blend{(\bOn)+(\cOn)+(\dOn)+(\eOn)}(A);
        }
      }
    }
  }
  \foreach \aOn in {Z,A}{
    \foreach \cOn in {Z,C}{
      \foreach \dOn in {Z,D}{
        \foreach \eOn in {Z,E}{
          \blend{(\aOn)+(\cOn)+(\dOn)+(\eOn)}(B);
        }
      }
    }
    \foreach \bOn in {Z,B}{
      \foreach \dOn in {Z,D}{
        \foreach \eOn in {Z,E}{
          \blend{(\aOn)+(\bOn)+(\dOn)+(\eOn)}(C);
        }
      }
      \foreach \cOn in {Z,C}{
        \foreach \eOn in {Z,E}{
          \blend{(\aOn)+(\bOn)+(\cOn)+(\eOn)}(D);
        }
        \foreach \dOn in {Z,D}{
          \blend{(\aOn)+(\bOn)+(\cOn)+(\dOn)}(E)node{};
          \draw($(\aOn)+(\bOn)+(\cOn)+(\dOn)$)node{};
        }
      }
    }
  }
  \foreach \unfaithfulNode in {Z,D,E} {
    \draw(\unfaithfulNode)node[cross]{};
  }
  \draw($(D)+(E)$)node[cross]{};
\end{tikzpicture}
\end{document}
Author AquitaneHungerForce

Licensing edit

I, the copyright holder of this work, hereby publish it under the following license:
w:en:Creative Commons
attribution share alike
This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.
You are free:
  • to share – to copy, distribute and transmit the work
  • to remix – to adapt the work
Under the following conditions:
  • attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
  • share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.

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Date/TimeThumbnailDimensionsUserComment
current21:08, 28 December 2023Thumbnail for version as of 21:08, 28 December 2023890 × 739 (144 KB)AquitaneHungerForce (talk | contribs)Fixed faithful realizations.
21:02, 28 December 2023Thumbnail for version as of 21:02, 28 December 2023890 × 739 (144 KB)AquitaneHungerForce (talk | contribs){{Information |Description = {{en|Symmetric realizations of the dodecahedron (or its Petrial). Crossed nodes indicate a non-faithful realization. Edges represent blending by a pure realization. Parallel edges, or edges of the same color/style correspond to blends by the same polyhedron. This is the Hasse diagram on the lattice formed with blending as the meet.}} |Source = {{Igen|LaTeX|v|code=<nowiki>\documentclass{standalone} \usepackage{tikz} \usetikzlibrary{decorations.pathmorphing,calc} \...

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