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\begin{tikzpicture}[x={(-0.5cm,-0.5cm)},y={(1cm,0cm)}, z={(0cm,1cm)}]
 
%3D-Koordinatensystem:
\draw[->, >=latex] (0,0,0) -- (3,0,0) node[left]{$zustand$};
\draw[->, >=latex] (0,0,0) -- (0,3,0) node[below]{$y$};
\draw[->, >=latex] (0,0,0) -- (0,0,3) node[left]{$z$};
 
 %\draw[densely dashed]  plot[] coordinates{(2,0,0)(2,2,0)(0,2,0)(0,0,2)};	
 
\shadedraw  plot [only marks, mark=*, mark size=1.5pt, mark options={fill=grey}] coordinates{
(1,1,1)
(1,1,0)(2,1,0)(3,1,0) %y1
(1,1,1)(2,1,1)(3,1,1)
(1,1,2)(2,1,2)(3,1,2)
(1,2,0)(2,2,0)(3,2,0) % y2
(1,2,1)(2,2,1)(3,2,1)
(1,2,2)(2,2,2)(3,2,2)
(1,3,0)(2,3,0)(3,3,0) % y3
(1,3,1)(2,3,1)(3,3,1)
(1,3,2)(2,3,2)(3,3,2)
};	
 \end{tikzpicture}

\begin{figure}[H]
\setlength\figurewidth{0.8\textwidth}
\centering
\begin{tikzpicture}[x={(0.7cm,0.7cm)},y={(1cm,0cm)}, z={(0cm,1cm)}]
 
%3D-Koordinatensystem:
\draw[->, >=latex] (0,0,0) -- (4,0,0) node[above]{$S$};
\draw[->, >=latex] (0,0,0) -- (0,14,0) node[below]{$y$};
\draw[->, >=latex] (0,0,0) -- (0,0,6) node[left]{$z$};
 
 %\draw[densely dashed]  plot[] coordinates{(2,0,0)(2,2,0)(0,2,0)(0,0,2)};	
\draw [dotted] plot[] coordinates{(1,1,0)(2,1,0)(3,1,0)};
\draw [dotted] plot[] coordinates{(1,1,2.5)(2,1,2.5)(3,1,2.5)};
\draw [dotted] plot[] coordinates{(1,1,5)(2,1,5)(3,1,5)};
\draw [dotted] plot[] coordinates{(1,4.5,0)(2,4.5,0)(3,4.5,0)};
\draw [dotted] plot[] coordinates{(1,4.5,2.5)(2,4.5,2.5)(3,4.5,2.5)};
\draw [dotted] plot[] coordinates{(1,4.5,5)(2,4.5,5)(3,4.5,5)};
\draw [dotted] plot[] coordinates{(1,8,0)(2,8,0)(3,8,0)};
\draw [dotted] plot[] coordinates{(1,8,2.5)(2,8,2.5)(3,8,2.5)};
\draw [dotted] plot[] coordinates{(1,8,5)(2,8,5)(3,8,5)};
\draw [dotted] plot[] coordinates{(1,1,0)(1,1,2.5)(1,1,5)};
\draw [dotted] plot[] coordinates{(2,1,0)(2,1,2.5)(2,1,5)};
\draw [dotted] plot[] coordinates{(3,1,0)(3,1,2.5)(3,1,5)};
\draw [dotted] plot[] coordinates{(1,4.5,0)(1,4.5,2.5)(1,4.5,5)};
\draw [dotted] plot[] coordinates{(2,4.5,0)(2,4.5,2.5)(2,4.5,5)};
\draw [dotted] plot[] coordinates{(3,4.5,0)(3,4.5,2.5)(3,4.5,5)};
\draw [dotted] plot[] coordinates{(1,8,0)(1,8,2.5)(1,8,5)};
\draw [dotted] plot[] coordinates{(2,8,0)(2,8,2.5)(2,8,5)};
\draw [dotted] plot[] coordinates{(3,8,0)(3,8,2.5)(3,8,5)};
\draw [dotted] plot[] coordinates{(1,11.5,0)(1,11.5,2.5)(1,11.5,5)};%high
\draw [dotted] plot[] coordinates{(2,11.5,0)(2,11.5,2.5)(2,11.5,5)};
\draw [dotted] plot[] coordinates{(3,11.5,0)(3,11.5,2.5)(3,11.5,5)};
\draw [dotted] plot[] coordinates{(1,0,0)(1,11.5,0)}; % horizontal
\draw [dotted] plot[] coordinates{(2,0,0)(2,11.5,0)};
\draw [dotted] plot[] coordinates{(3,0,0)(3,11.5,0)};
\draw [dotted] plot[] coordinates{(1,0,2.5)(1,11.5,2.5)};
\draw [dotted] plot[] coordinates{(2,0,2.5)(2,11.5,2.5)};
\draw [dotted] plot[] coordinates{(3,0,2.5)(3,11.5,2.5)};
\draw [dotted] plot[] coordinates{(1,0,5)(1,11.5,5)};
\draw [dotted] plot[] coordinates{(2,0,5)(2,11.5,5)};
\draw [dotted] plot[] coordinates{(3,0,5)(3,11.5,5)};
%\draw [dotted] plot[] coordinates{(1,0,0)(3,0,0)};
\draw [dotted] plot[] coordinates{(1,0,2.5)(3,0,2.5)};
\draw [dotted] plot[] coordinates{(1,0,5)(3,0,5)};
\draw [dotted] plot[] coordinates{(1,0,0)(1,0,5)};
\draw [dotted] plot[] coordinates{(2,0,0)(2,0,5)};
\draw [dotted] plot[] coordinates{(3,0,0)(3,0,5)};
\draw [dotted] plot[] coordinates{(1,11.5,0)(3,11.5,0)};
\draw [dotted] plot[] coordinates{(1,11.5,2.5)(3,11.5,2.5)};
\draw [dotted] plot[] coordinates{(1,11.5,5)(3,11.5,5)};
 %(1,1,0)(1,1,2.5)(1,1,5)
\shadedraw  plot [only marks, mark=*, mark size=4.5pt, mark options={fill=gray}] coordinates{
(1,1,0)(2,1,0)(3,1,0) %y1
(1,1,2.5)(2,1,2.5)(3,1,2.5)
(1,1,5)(2,1,5)(3,1,5)
(1,4.5,0)(2,4.5,0)(3,4.5,0) % y2
(1,4.5,2.5)(2,4.5,2.5)(3,4.5,2.5)
(1,4.5,5)(2,4.5,5)(3,4.5,5)
(1,8,0)(2,8,0)(3,8,0) % y3
(1,8,2.5)(2,8,2.5)(3,8,2.5)
(1,8,5)(2,8,5)(3,8,5)
(2,11.5,2.5)
};	
 \end{tikzpicture}
\caption{3D-DDP}
\label{img:3D-DDP}
\end{figure}