Fill a polydedron with 3dtools - TeX

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4 years ago user 3.14159

If you do not insist on transformed patterns, then everything is already part to the 3dtools library. You just change the fore style for some of the faces.

\documentclass[tikz,border=3.14mm]{standalone}
\usetikzlibrary{calc,3dtools}% https://github.com/marmotghost/tikz-3dtools
\begin{document}
\begin{tikzpicture}[3d/install view={phi=20,theta=70},line join = round, 
	line cap = round, declare function={a =2;},same bounding box=A,
	c/.style={circle,fill,inner sep=1pt}]
   \path
   (-a,-a,-a) coordinate (A)
   (a,-a,-a) coordinate (B)
   (a,a,-a) coordinate (C)
   (-a,a,-a) coordinate (D)
   (-a,-a,a) coordinate (A')
   (a,-a,a) coordinate (B')
   (a,a,a) coordinate (C')
   (-a,a,a) coordinate (D')
   (a,0,-a) coordinate (K)
   (a,-a,0) coordinate (M);
   \tikzset{fore'/.style={fill opacity=0.5,draw,solid},
    3d/polyhedron/.cd,O={(0,0,0)},fore/.style={fore',fill=none},
   	back/.append style={3d/hidden},
   	draw face with corners={{(B)},{(K)},{(M)}},
   	draw face with corners={{(A)},{(B)},{(M)},{(A')}},
   	draw face with corners={{(A)},{(D)},{(A')}},
   	draw face with corners={{(D)},{(D')},{(A')}},
   	draw face with corners={{(D)},{(D')},{(C')},{(C)}},
	fore/.style={fore',fill=gray!50},
   	draw face with corners={{(A')},{(M)},{(B')}},
	draw face with corners={{(A')},{(B')},{(C')},{(D')}},
   	draw face with corners={{(K)},{(C)},{(C')},{(B')},{(M)},{(K)}},
	fore/.style={fore',draw=none,fill=blue!50},
   	draw face with corners={{(A')},{(D)},{(K)},{(M)}}
	}
	\draw[3d/hidden] (D) -- (K);
	\path foreach \X in {A,...,D} {(\X) node[c,label={below:$\X$}]{}
		(\X') node[c,label={above:$\X'$}]{}}
		foreach \X in {K,M} {(\X) node[c,label={above:$\X$}]{}};
\end{tikzpicture}
\end{document}

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\documentclass[tikz,border=3.14mm]{standalone}\usetikzlibrary{calc,3dtools}% https://github.com/marmotghost/tikz-3dtools\begin{document}\begin{tikzpicture}[3d/install view={phi=20,theta=70},line join = round,     line cap = round, declare function={a =2;},same bounding box=A,    c/.style={circle,fill,inner sep=1pt}]   \path   (-a,-a,-a) coordinate (A)   (a,-a,-a) coordinate (B)   (a,a,-a) coordinate (C)   (-a,a,-a) coordinate (D)   (-a,-a,a) coordinate (A')   (a,-a,a) coordinate (B')   (a,a,a) coordinate (C')   (-a,a,a) coordinate (D')   (a,0,-a) coordinate (K)   (a,-a,0) coordinate (M);   \tikzset{fore'/.style={fill opacity=0.5,draw,solid},    3d/polyhedron/.cd,O={(0,0,0)},fore/.style={fore',fill=none},    back/.append style={3d/hidden},    draw face with corners={{(B)},{(K)},{(M)}},    draw face with corners={{(A)},{(B)},{(M)},{(A')}},    draw face with corners={{(A)},{(D)},{(A')}},    draw face with corners={{(D)},{(D')},{(A')}},    draw face with corners={{(D)},{(D')},{(C')},{(C)}},    fore/.style={fore',fill=gray!50},    draw face with corners={{(A')},{(M)},{(B')}},    draw face with corners={{(A')},{(B')},{(C')},{(D')}},    draw face with corners={{(K)},{(C)},{(C')},{(B')},{(M)},{(K)}},    fore/.style={fore',draw=none,fill=blue!50},    draw face with corners={{(A')},{(D)},{(K)},{(M)}}    }    \draw[3d/hidden] (D) -- (K);    \path foreach \X in {A,...,D} {(\X) node[c,label={below:$\X$}]{}        (\X') node[c,label={above:$\X'$}]{}}        foreach \X in {K,M} {(\X) node[c,label={above:$\X$}]{}};\end{tikzpicture}\end{document}  
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Obviously you can also use patterns from patterns.meta, say, to shade the faces. What won’t happen there is that the patterns get transformed to the plane. In fact, even though it is straightforward to project pretty much anything on a plane, this is not the case for patterns, which are some low-level directives that directly talk to the driver (which is why, among other things, they may look different on a pdf and a pdf that has been converted to a bitmap, say). You can define (computationally expensive) pattern-like styles and project those. I copied a style from this post and slightly modified it to provide you with an explicit example. This pattern gets projected “obvious” planes like the xy plane from the 3d library but also on a slightly less obvious one.

\documentclass[tikz,border=3mm]{standalone}
\usetikzlibrary{calc,3dtools}% https://github.com/marmotghost/tikz-3dtools
\tikzset{manual pattern/.style={manual pattern keys/.cd,#1,
	/tikz/path picture={
	\pgfmathsetmacro{\mybeta}{Mod(270+\pgfkeysvalueof{/tikz/manual pattern keys/angle},180)-90}
	\pgfmathtruncatemacro{\myt}{\mybeta<-45?0:(\mybeta<0?1:(\mybeta<45?2:3))}
	\def\myxshift{0pt}
	\def\myyshift{0pt}
	\ifcase\myt
	 \pgfmathsetmacro{\mydelta}{abs(cos(\mybeta))}
	 \pgfmathsetmacro{\myd}{1/abs(sin(\mybeta))}
	 \def\mystart{path picture bounding box.north west}
	 \def\myxshift{-\y1*\mydelta+\z*\pgfkeysvalueof{/tikz/manual pattern keys/distance}*\myd}
	\or 
	 \pgfmathsetmacro{\mydelta}{abs(sin(\mybeta))}
	 \pgfmathsetmacro{\myd}{1/abs(cos(\mybeta))}
	 \def\mystart{path picture bounding box.north west}
	 \def\myyshift{\x1*\mydelta-\z*\pgfkeysvalueof{/tikz/manual pattern keys/distance}*\myd}
	\or 
	 \pgfmathsetmacro{\mydelta}{abs(sin(\mybeta))}
	 \pgfmathsetmacro{\myd}{1/abs(cos(\mybeta))}
	 \def\mystart{path picture bounding box.south west}
	 \def\myyshift{-\x1*\mydelta+\z*\pgfkeysvalueof{/tikz/manual pattern keys/distance}*\myd}
	\or 
	 \pgfmathsetmacro{\mydelta}{abs(cos(\mybeta))}
	 \pgfmathsetmacro{\myd}{1/abs(sin(\mybeta))}
	 \def\mystart{path picture bounding box.south west}
	 \def\myxshift{-\y1*\mydelta+\z*\pgfkeysvalueof{/tikz/manual pattern keys/distance}*\myd}
	\fi
	\path
	let \p1=($(path picture bounding box.north east)-(path picture bounding box.south west)$),
	\n1={scalar(int(1+2*(\x1+\y1)/\pgfkeysvalueof{/tikz/manual pattern keys/distance}))},
	\n2={max(\x1,\y1)*sqrt(2)}
	in foreach \z in {-\n1,...,\n1}
	{([xshift=\myxshift,yshift=\myyshift]\mystart)
	 edge[/tikz/manual pattern keys/lines] ++ (\mybeta:\n2)
	};
}},manual pattern keys/.cd,distance/.initial=5pt,angle/.initial=-45,
	lines/.style={draw}}
\begin{document}
\begin{tikzpicture}[3d/install view={phi=20,theta=70},line join = round, 
	line cap = round, declare function={a =2;},
	c/.style={circle,fill,inner sep=1pt},
	same bounding box=A]
   \path
   (-a,-a,-a) coordinate (A)
   (a,-a,-a) coordinate (B)
   (a,a,-a) coordinate (C)
   (-a,a,-a) coordinate (D)
   (-a,-a,a) coordinate (A')
   (a,-a,a) coordinate (B')
   (a,a,a) coordinate (C')
   (-a,a,a) coordinate (D')
   (a,0,-a) coordinate (K)
   (a,-a,0) coordinate (M);
   \tikzset{3d/define orthonormal dreibein={A={(K)},B={(D)},C={(A')}}}
   \begin{scope}[x={(ex)},y={(ey)},z={(ez)}]
	\path[manual pattern={lines/.style=3d/hidden}] (D) -- (A') -- (M) -- (K) -- cycle;
   \end{scope}
   \draw[3d/hidden] (D) -- (K);
   \begin{scope}[canvas is xz plane at y=-a]
    \path[manual pattern] (A') -- (M) -- (B') -- cycle;
   \end{scope}	
   \begin{scope}[canvas is yz plane at x=a]
    \path[manual pattern] (K) -- (C) -- (C') -- (B') -- (M) -- cycle;
   \end{scope}	
   \begin{scope}[canvas is xy plane at z=a]
    \path[manual pattern] (A') -- (B') -- (C') -- (D') -- cycle;
   \end{scope}	
   \tikzset{3d/polyhedron/.cd,O={(0,0,0)},fore/.append style={fill=none},
   	back/.append style={3d/hidden},
   	draw face with corners={{(A')},{(B')},{(C')},{(D')}},
   	draw face with corners={{(A)},{(B)},{(M)},{(A')}},
   	draw face with corners={{(A')},{(M)},{(B')}},
   	draw face with corners={{(A)},{(D)},{(A')}},
   	draw face with corners={{(D)},{(D')},{(A')}},
   	draw face with corners={{(D)},{(D')},{(C')},{(C)}},
   	draw face with corners={{(K)},{(C)},{(C')},{(B')},{(M)},{(K)}},
   	draw face with corners={{(B)},{(K)},{(M)}}}
   \path foreach \X in {A,...,D} {(\X) node[c,label={below:$\X$}]{}
		(\X') node[c,label={above:$\X'$}]{}}
		foreach \X in {K,M} {(\X) node[c,label={above:$\X$}]{}};
\end{tikzpicture}
\end{document}

xxxxxxxxxx
 
\documentclass[tikz,border=3mm]{standalone}\usetikzlibrary{calc,3dtools}% https://github.com/marmotghost/tikz-3dtools\tikzset{manual pattern/.style={manual pattern keys/.cd,#1,    /tikz/path picture={    \pgfmathsetmacro{\mybeta}{Mod(270+\pgfkeysvalueof{/tikz/manual pattern keys/angle},180)-90}    \pgfmathtruncatemacro{\myt}{\mybeta<-45?0:(\mybeta<0?1:(\mybeta<45?2:3))}    \def\myxshift{0pt}    \def\myyshift{0pt}    \ifcase\myt     \pgfmathsetmacro{\mydelta}{abs(cos(\mybeta))}     \pgfmathsetmacro{\myd}{1/abs(sin(\mybeta))}     \def\mystart{path picture bounding box.north west}     \def\myxshift{-\y1*\mydelta+\z*\pgfkeysvalueof{/tikz/manual pattern keys/distance}*\myd}    \or      \pgfmathsetmacro{\mydelta}{abs(sin(\mybeta))}     \pgfmathsetmacro{\myd}{1/abs(cos(\mybeta))}     \def\mystart{path picture bounding box.north west}     \def\myyshift{\x1*\mydelta-\z*\pgfkeysvalueof{/tikz/manual pattern keys/distance}*\myd}    \or      \pgfmathsetmacro{\mydelta}{abs(sin(\mybeta))}     \pgfmathsetmacro{\myd}{1/abs(cos(\mybeta))}     \def\mystart{path picture bounding box.south west}     \def\myyshift{-\x1*\mydelta+\z*\pgfkeysvalueof{/tikz/manual pattern keys/distance}*\myd}    \or      \pgfmathsetmacro{\mydelta}{abs(cos(\mybeta))}     \pgfmathsetmacro{\myd}{1/abs(sin(\mybeta))}     \def\mystart{path picture bounding box.south west}     \def\myxshift{-\y1*\mydelta+\z*\pgfkeysvalueof{/tikz/manual pattern keys/distance}*\myd}    \fi    \path    let \p1=($(path picture bounding box.north east)-(path picture bounding box.south west)$),    \n1={scalar(int(1+2*(\x1+\y1)/\pgfkeysvalueof{/tikz/manual pattern keys/distance}))},    \n2={max(\x1,\y1)*sqrt(2)}    in foreach \z in {-\n1,...,\n1}    {([xshift=\myxshift,yshift=\myyshift]\mystart)     edge[/tikz/manual pattern keys/lines] ++ (\mybeta:\n2)    };}},manual pattern keys/.cd,distance/.initial=5pt,angle/.initial=-45,    lines/.style={draw}}\begin{document}\begin{tikzpicture}[3d/install view={phi=20,theta=70},line join = round,     line cap = round, declare function={a =2;},    c/.style={circle,fill,inner sep=1pt},    same bounding box=A]   \path   (-a,-a,-a) coordinate (A)   (a,-a,-a) coordinate (B)   (a,a,-a) coordinate (C)   (-a,a,-a) coordinate (D)   (-a,-a,a) coordinate (A')   (a,-a,a) coordinate (B')   (a,a,a) coordinate (C')   (-a,a,a) coordinate (D')   (a,0,-a) coordinate (K)   (a,-a,0) coordinate (M);   \tikzset{3d/define orthonormal dreibein={A={(K)},B={(D)},C={(A')}}}   \begin{scope}[x={(ex)},y={(ey)},z={(ez)}]    \path[manual pattern={lines/.style=3d/hidden}] (D) -- (A') -- (M) -- (K) -- cycle;   \end{scope}   \draw[3d/hidden] (D) -- (K);   \begin{scope}[canvas is xz plane at y=-a]    \path[manual pattern] (A') -- (M) -- (B') -- cycle;   \end{scope}     \begin{scope}[canvas is yz plane at x=a]    \path[manual pattern] (K) -- (C) -- (C') -- (B') -- (M) -- cycle;   \end{scope}     \begin{scope}[canvas is xy plane at z=a]    \path[manual pattern] (A') -- (B') -- (C') -- (D') -- cycle;   \end{scope}     \tikzset{3d/polyhedron/.cd,O={(0,0,0)},fore/.append style={fill=none},    back/.append style={3d/hidden},    draw face with corners={{(A')},{(B')},{(C')},{(D')}},    draw face with corners={{(A)},{(B)},{(M)},{(A')}},    draw face with corners={{(A')},{(M)},{(B')}},    draw face with corners={{(A)},{(D)},{(A')}},    draw face with corners={{(D)},{(D')},{(A')}},    draw face with corners={{(D)},{(D')},{(C')},{(C)}},    draw face with corners={{(K)},{(C)},{(C')},{(B')},{(M)},{(K)}},    draw face with corners={{(B)},{(K)},{(M)}}}   \path foreach \X in {A,...,D} {(\X) node[c,label={below:$\X$}]{}        (\X') node[c,label={above:$\X'$}]{}}        foreach \X in {K,M} {(\X) node[c,label={above:$\X$}]{}};\end{tikzpicture}\end{document}    
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