% !TeX TXS-program:compile = txs:///pdflatex

\documentclass[margin=5mm]{standalone}
\usepackage{tikz}
\usetikzlibrary{calc}
\usepackage{esvect}

\begin{document}

	\begin{tikzpicture}[x={(-160:0.4cm)},y={(-15:0.52cm)},z={(90:0.52cm)},line join=bevel]
		\coordinate (O) at (0,0,0) ; \draw (O) node[below] {$O$} ;
		\coordinate (B) at (6,0,0) ; \draw (B) node[below left] {$B$} ;
		\coordinate (D) at (0,8,0) ; \draw (D) node[below right] {$D$} ;
		\coordinate (C) at (6,8,0) ; \draw (C) node[below] {$C$} ;
		\coordinate (E) at (0,0,4) ; \draw (E) node[above] {$E$} ;
		\coordinate (F) at (6,0,4) ; \draw (F) node[above left] {$F$} ;
		\coordinate (H) at (0,8,4) ; \draw (H) node[above right] {$H$} ;
		\coordinate (G) at (6,8,4) ; \draw (G) node[below right] {$G$} ;
		\draw[thick,->,>=latex] (O)--++(1,0,0) node[above left=0pt,font=\small] {$\vv{\imath}$} ;
		\draw[thick,->,>=latex] (O)--++(0,1,0) node[above right=0pt,font=\small] {$\vv{\jmath}$} ;
		\draw[thick,->,>=latex] (O)--++(0,0,1) node[left=0pt,font=\small] {$\vv{k}$} ;
		\draw[semithick,densely dashed] (O)--(B) (E)--(O)--(D) ;
		\draw[semithick] (B)--(F)--(G)--(C)--cycle (F)--(E)--(H)--(G)--cycle (C)--(D)--(H) ;
		%autres points et tracés
		\coordinate (A) at (6,0,2) ; \draw (A) node[left] {$A$} ;
		\coordinate (R) at (6,3,4) ; \draw (R) node[above right] {$R$} ;
		\coordinate (T) at (3,0,4) ; \draw (T) node[above] {$T$} ;
		\coordinate (S) at (3,2.5,0) ;
		\draw[thick] (A)--(R)--(T) ; \draw[thick,densely dashed] (A)--(T) ;
		\coordinate (L) at (5,0.5,3) ;
		\coordinate (K) at ($(E)!0.5!(H)$) ; \draw (K) node[above] {$K$} ;
		\draw[semithick,densely dashed] (K)--(D) ;
		\coordinate (N) at (0,{23/5},{17/5}) ; 
		\draw[thick,red] (L)--(S)--(N) ;
		%point labélisés
		\filldraw (N) circle[radius=1.5pt] node[right] {$N$} ;
		\filldraw (L) circle[radius=1.5pt] node[below] {$L$} ;
		\filldraw (S) circle[radius=1.5pt] node[below] {$S$} ;
	\end{tikzpicture}

\end{document}