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

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

\begin{document}

\begin{tikzpicture}[x={(0:4cm)},y={(27:2cm)},z={(90:4cm)},line join=bevel]
	\coordinate (A) at (0,0,0) ; \coordinate (B) at (1,0,0) ;
	\coordinate (C) at (1,1,0) ; \coordinate (D) at (0,1,0) ;
	\coordinate (E) at (0,0,1) ; \coordinate (F) at (1,0,1) ;
	\coordinate (G) at (1,1,1) ; \coordinate (H) at (0,1,1) ;
	\coordinate (I) at ({2/3},{2/3},{1/3}) ;
	\coordinate (J) at ($(D)!0.5!(B)$) ;
	\coordinate (U) at ($(E)!-0.16!(C)$) ;%prolongement de (EC) à gauche
	\coordinate (V) at ($(E)!1.19!(C)$) ;%prolongement de (EC) à droite
	\draw[semithick,dashed] (A)--(D)--(C) (D)--(H) ;
	\draw[semithick,densely dashed] (D)--(B) (E)--(C) (D)--(G) ;
	\draw[semithick] (A)--(B)--(F)--(E)--cycle  (B)--(C)--(G)--(F)--cycle (E)--(F)--(G)--(H)--cycle (B)--(G) (U)--(E) (C)--(V) ;
	\foreach \point/\pos in {A/below,B/below,C/below,D/below,E/above,F/above,G/above,H/above,I/below left,J/below left}
		{\filldraw (\point) circle[radius=1.25pt] node[\pos] {$\point$} ;}
\end{tikzpicture}

\end{document}