How can I fill this pyramid like this picture?

Question

How can I fill this pyramid like this picture? (with GeoSpacW)

I tried (with GeoGebra)

\documentclass[12pt]{standalone}
\usepackage{fouriernc}
\usepackage{pgf,tikz}
\usepackage{mathrsfs}
\usetikzlibrary{arrows}
\pagestyle{empty}
\begin{document}
\begin{tikzpicture}[line cap=round,line join=round,>=triangle 45,x=1.0cm,y=1.0cm]
\clip(-0.5165217391304349,-3.515177065767286) rectangle (8.983478260869564,5.484822934232715);
\draw [line width=1.2pt] (1.9204347826086954,4.665261382799326)-- (0.,0.);
\draw [line width=1.2pt] (1.9204347826086954,4.665261382799326)-- (2.,-3.);
\draw [line width=1.2pt] (1.9204347826086954,4.665261382799326)-- (6.,-3.);
\draw [line width=1.2pt] (1.9204347826086954,4.665261382799326)-- (8.,0.);
\draw [line width=1.2pt] (8.,0.)-- (6.,-3.);
\draw [line width=1.2pt] (6.,-3.)-- (2.,-3.);
\draw [line width=1.2pt] (2.,-3.)-- (0.,0.);
\draw [dash pattern=on 2pt off 2pt] (0.,0.)-- (8.,0.);
\draw [dash pattern=on 2pt off 2pt] (0.,0.)-- (6.,-3.);
\draw [dash pattern=on 2pt off 2pt] (4.960217391304347,2.332630691399663)-- (1.,-1.5);
\draw [line width=1.2pt] (1.9204347826086954,4.665261382799326)-- (1.,-1.5);
\draw [dash pattern=on 2pt off 2pt] (1.,-1.5)-- (8.,0.);
\draw [dash pattern=on 2pt off 2pt] (1.,-1.5)-- (4.,-3.);
\draw [dash pattern=on 2pt off 2pt] (1.9204347826086954,4.665261382799326)-- (2.4,-1.2);
\draw [dash pattern=on 2pt off 2pt] (0.3200724637681158,0.7775435637998873)-- (4.960217391304347,2.332630691399663);
\draw [line width=1.2pt] (4.960217391304347,2.332630691399663)-- (5.320072463768115,-1.7224564362001122);
\draw [line width=1.2pt] (5.320072463768115,-1.7224564362001122)-- (4.,-3.);
\draw [line width=1.2pt] (1.,-1.5)-- (0.3200724637681158,0.7775435637998873);
\draw [dash pattern=on 2pt off 2pt] (0.3200724637681158,0.7775435637998873)-- (5.320072463768115,-1.7224564362001122);
\draw [fill=black] (0.,0.) circle (1.5pt);
\draw[color=black] (-0.12826086956521748,-0.25210792580101227) node {$A$};
\draw [fill=black] (8.,0.) circle (1.5pt);
\draw[color=black] (8.25,0.15) node {$B$};
\draw [fill=black] (6.,-3.) circle (1.5pt);
\draw[color=black] (6.0260869565217385,-3.2116357504215856) node {$C$};
\draw [fill=black] (2.,-3.) circle (1.5pt);
\draw[color=black] (1.928695652173913,-3.2116357504215856) node {$D$};
\draw [fill=black] (1.9204347826086954,4.665261382799326) circle (1.5pt);
\draw[color=black] (1.978260869565217,4.877740303541315) node {$S$};
\draw [fill=black] (1.,-1.5) circle (1.5pt);
\draw[color=black] (0.8,-1.7242833052276565) node {$M$};
\draw [fill=black] (4.960217391304347,2.332630691399663) circle (1.5pt);
\draw[color=black] (5.018260869565217,2.6) node {$N$};
\draw [fill=black] (4.,-3.) circle (1.5pt);
\draw[color=black] (3.944347826086956,-3.226812816188871) node {$E$};
\draw [fill=black] (2.4,-1.2) circle (1.5pt);
\draw[color=black] (2.399565217391304,-1.45) node {$O$};
\draw [fill=black] (2.320072463768116,-0.2224564362001124) circle (1.5pt);
\draw[color=black] (2.250869565217391,-0.5101180438448571) node {$I$};
\draw [fill=black] (0.3200724637681158,0.7775435637998873) circle (1.5pt);
\draw[color=black] (0.2186956521739129,1.0379426644182121) node {$G$};
\draw [fill=black] (5.320072463768115,-1.7224564362001122) circle (1.5pt);
\draw[color=black] (5.5,-1.5118043844856666) node {$F$};
\end{tikzpicture}
\end{document}

and got

I assume the picture represents a pyramid that has been cut by a plane going through the points EFNGM, correct? — Werner, Dec 10, 2015 at 4:31
Would it be ok to use a transparent color (fill) instead of a pattern? It would sure be easier. — John Kormylo, Dec 10, 2015 at 5:53

Ignasi · Accepted Answer · 2015-12-10 10:40:22Z

Add coordinates where geogebra define vertices (circle (1.5pt)), like

\draw [fill=black] (0.,0.) circle (1.5pt) coordinate (A);

and fill the desired closed area with your preferred pattern

\path[pattern=vertical lines, pattern color=red] (G)--(M)--(E)--(F)--(N)--cycle;

The complete code:

\documentclass[12pt]{standalone}
\usepackage{fouriernc}
\usepackage{pgf,tikz}
\usepackage{mathrsfs}
\usetikzlibrary{arrows,patterns}
\pagestyle{empty}
\begin{document}
\begin{tikzpicture}[line cap=round,line join=round,>=triangle 45,x=1.0cm,y=1.0cm]
\clip(-0.5165217391304349,-3.515177065767286) rectangle (8.983478260869564,5.484822934232715);
\draw [line width=1.2pt] (1.9204347826086954,4.665261382799326)-- (0.,0.);
\draw [line width=1.2pt] (1.9204347826086954,4.665261382799326)-- (2.,-3.);
\draw [line width=1.2pt] (1.9204347826086954,4.665261382799326)-- (6.,-3.);
\draw [line width=1.2pt] (1.9204347826086954,4.665261382799326)-- (8.,0.);
\draw [line width=1.2pt] (8.,0.)-- (6.,-3.);
\draw [line width=1.2pt] (6.,-3.)-- (2.,-3.);
\draw [line width=1.2pt] (2.,-3.)-- (0.,0.);
\draw [dash pattern=on 2pt off 2pt] (0.,0.)-- (8.,0.);
\draw [dash pattern=on 2pt off 2pt] (0.,0.)-- (6.,-3.);
\draw [dash pattern=on 2pt off 2pt] (4.960217391304347,2.332630691399663)-- (1.,-1.5);
\draw [line width=1.2pt] (1.9204347826086954,4.665261382799326)-- (1.,-1.5);
\draw [dash pattern=on 2pt off 2pt] (1.,-1.5)-- (8.,0.);
\draw [dash pattern=on 2pt off 2pt] (1.,-1.5)-- (4.,-3.);
\draw [dash pattern=on 2pt off 2pt] (1.9204347826086954,4.665261382799326)-- (2.4,-1.2);
\draw [dash pattern=on 2pt off 2pt] (0.3200724637681158,0.7775435637998873)-- (4.960217391304347,2.332630691399663);
\draw [line width=1.2pt] (4.960217391304347,2.332630691399663)-- (5.320072463768115,-1.7224564362001122);
\draw [line width=1.2pt] (5.320072463768115,-1.7224564362001122)-- (4.,-3.);
\draw [line width=1.2pt] (1.,-1.5)-- (0.3200724637681158,0.7775435637998873);
\draw [dash pattern=on 2pt off 2pt] (0.3200724637681158,0.7775435637998873)-- (5.320072463768115,-1.7224564362001122);
\draw [fill=black] (0.,0.) circle (1.5pt) coordinate (A);
\draw[color=black] (-0.12826086956521748,-0.25210792580101227) node {$A$};
\draw [fill=black] (8.,0.) circle (1.5pt) coordinate (B);
\draw[color=black] (8.25,0.15) node {$B$};
\draw [fill=black] (6.,-3.) circle (1.5pt) coordinate (C);
\draw[color=black] (6.0260869565217385,-3.2116357504215856) node {$C$};
\draw [fill=black] (2.,-3.) circle (1.5pt) coordinate (D);
\draw[color=black] (1.928695652173913,-3.2116357504215856) node {$D$};
\draw [fill=black] (1.9204347826086954,4.665261382799326) circle (1.5pt) coordinate (S);
\draw[color=black] (1.978260869565217,4.877740303541315) node {$S$};
\draw [fill=black] (1.,-1.5) circle (1.5pt) coordinate (M);
\draw[color=black] (0.8,-1.7242833052276565) node {$M$};
\draw [fill=black] (4.960217391304347,2.332630691399663) circle (1.5pt) coordinate (N);
\draw[color=black] (5.018260869565217,2.6) node {$N$};
\draw [fill=black] (4.,-3.) circle (1.5pt) coordinate (E);
\draw[color=black] (3.944347826086956,-3.226812816188871) node {$E$};
\draw [fill=black] (2.4,-1.2) circle (1.5pt) coordinate (O);
\draw[color=black] (2.399565217391304,-1.45) node {$O$};
\draw [fill=black] (2.320072463768116,-0.2224564362001124) circle (1.5pt) coordinate (I);
\draw[color=black] (2.250869565217391,-0.5101180438448571) node {$I$};
\draw [fill=black] (0.3200724637681158,0.7775435637998873) circle (1.5pt) coordinate (G);
\draw[color=black] (0.2186956521739129,1.0379426644182121) node {$G$};
\draw [fill=black] (5.320072463768115,-1.7224564362001122) circle (1.5pt) coordinate (F);
\draw[color=black] (5.5,-1.5118043844856666) node {$F$};
\path[pattern=vertical lines, pattern color=red] (G)--(M)--(E)--(F)--(N)--cycle;
\end{tikzpicture}
\end{document}

and the result:

@minthao_2011 If you use \path[pattern=... instead of \draw[red, pattern ... the area border is not drawn and original black dashed or solid lines are not covered. — Ignasi, Dec 10, 2015 at 8:37
I did. But I could not get style of segments ME and GN are dash. — minthao_2011, Dec 10, 2015 at 9:09
@minthao_2011 I've updated the code ans resulting figure. In code I've only changed third last line as in my previous comment. As you can see ME and GN are dashed lines. — Ignasi, Dec 10, 2015 at 10:42

minthao_2011 · Accepted Answer · 2015-12-11 05:25:42Z

I tried with tkz-euclide My code

\documentclass[border=2mm,12pt]{standalone}
\usepackage{fouriernc}
\usepackage{tkz-euclide,amsmath} 
\usetkzobj{all} 
\tikzset{hidden/.style = {thick, dotted}}
\begin{document}
\begin{tikzpicture}[scale=1]
\tkzDefPoints{0/0/A,
8/0/B,
6/-3/C,
2/-3/D,
1/5/S}
\tkzDefMidPoint(A,D)                      \tkzGetPoint{M}
\tkzDefMidPoint(S,B)                      \tkzGetPoint{N}
\tkzDefMidPoint(D,C)                      \tkzGetPoint{E}
\tkzInterLL(A,C)(M,B) \tkzGetPoint{O}
\tkzInterLL(M,N)(S,O) \tkzGetPoint{I}
\tkzDefLine[parallel=through I](A,C)
 \tkzGetPoint{d}
\tkzInterLL(d,I)(S,C) \tkzGetPoint{F}
\tkzInterLL(d,I)(S,A) \tkzGetPoint{G}
\tkzLabelPoints[right](B,C,I,F)
\tkzLabelPoints[left](A,D,M,G)
\tkzLabelPoints[above](S)
\tkzLabelPoints[below](O,E)
\tkzLabelPoints[above,right](N)
\tkzDrawPoints[color=black](A,B,C,D,S,M,N,O,I,F,G,E)
\tkzDrawSegments[hidden](A,B A,C M,N M,B S,O G,F M,E G,N)
\tkzDrawSegments(B,C C,D D,A S,A S,B S,C S,D S,M G,M E,F F,N)
\tkzFillPolygon[pattern color=red, pattern=vertical lines](G,M,E,F,N)
\end{tikzpicture}
\end{document}

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