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

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

\begin{document}

\begin{tikzpicture}[x={(-45:12.5mm)},y={(30:14mm)},z={(90:10mm)},line join=bevel]
	\coordinate (A) at (0,0,0) ;
	\coordinate (B) at (2,0,0) ;
	\coordinate (C) at (2,2,0) ;
	\coordinate (D) at (0,2,0) ;
	\coordinate (E) at (0,0,2) ;
	\coordinate (F) at (2,0,2) ;
	\coordinate (G) at (2,2,2) ;
	\coordinate (H) at (0,2,2) ;
	\coordinate (L) at (2,0,1) ;
	\coordinate (K) at (2,1,0) ;
	\coordinate (I) at (3,0,0) ;
	\coordinate (M) at (3,0,1) ;
	\coordinate (J) at (3,1,0) ;
	\coordinate (N) at (3,1,1) ;
	\coordinate (O) at (2,1,1) ;
	\coordinate (P) at (2,{2/3},{4/3}) ;
	\coordinate (Q) at (2,1.55,0) ;
	\fill[draw=none,semithick,fill=lightgray!25] (A)--(B)--(F)--(E)--cycle ;
	\fill[draw=none,semithick,fill=lightgray!25] (E)--(F)--(G)--(H)--cycle ;
	\fill[draw=none,semithick,fill=lightgray!25] (B)--(C)--(G)--(F)--cycle ;
	\fill[draw=none,semithick,fill=lightgray!25] (B)--(L)--(M)--(I)--cycle ;
	\fill[draw=none,semithick,fill=lightgray!25] (I)--(J)--(N)--(M)--cycle ;
	\fill[draw=none,semithick,fill=lightgray!75] (L)--(M)--(N)--(O)--(P)--cycle ;
	\draw[->,>=latex] (A)--(1,0,0) node[pos=0.4,below=2pt,font=\scriptsize] {$\vv{\imath}$} ;
	\draw[->,>=latex,densely dashed] (A)--(0,1,0) node[midway,above,font=\scriptsize] {$\vv{\jmath}$} ;
	\draw[->,>=latex] (A)--(0,0,1) node[midway,left,font=\scriptsize] {$\vv{k}$} ;
	\draw[thick] (A)--(B)--(F)--(E)--cycle ;
	\draw[thick] (E)--(F)--(G)--(H)--cycle ;
	\draw[thick] (B)--(F)--(G)--(C) ;
	\draw[thick,dashed] (B)--(C) (A)--(D)--(H) (D)--(C) (B)--(K)--(J);
	\draw[thick,gray] (L)--(M)--(N)--(O)--(P)--cycle (P)--(M) (P)--(N) ;
	\draw[thick,gray,dashed] (L)--(O)--(K) ;
	\draw[thick] (B)--(I)--(M)--(L)--cycle (Q)--(C)--(G) ;
	\draw[thick] (I)--(J)--(N)--(M)--cycle ;
	\draw[->,>=latex,semithick] (A)--(4,0,0) ;
	\draw[->,>=latex,semithick] (A)--(0,0,3) ;
	\draw[semithick,gray,densely dashed,] (D)--(0,3.05,0) ;
	\draw[->,>=latex,semithick] (0,3.05,0)--(0,4.5,0) ;
	\foreach \point/\pos in {A/left,B/below,C/right,D/above left,E/left,F/above,G/right,H/above,I/below,J/right,K/below,L/left,M/below right,N/above right,O/above,P/above}
		{\draw (\point) node[font=\scriptsize,\pos] {$\point$} ;}
\end{tikzpicture}
\end{document}