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

\documentclass[margin=5mm]{standalone}
\usepackage{tkz-euclide}

\begin{document}

\begin{tikzpicture}[scale=1,font=\small]
	\tkzDefPoint(0,0){A}\tkzDefPoint(4,-0.5){B}\tkzDefPoint(0,4.0311){E}\tkzDefPoint(4,3.5311){F}
	\begin{scope}[shift=(A)]\tkzDefPoint(1.5,1){D}\end{scope}
	\begin{scope}[shift=(B)]\tkzDefPoint(1.5,1){C}\end{scope}
	\begin{scope}[shift=(E)]\tkzDefPoint(1.5,1){H}\end{scope}
	\begin{scope}[shift=(F)]\tkzDefPoint(1.5,1){G}\end{scope}
	\tkzDefMidPoint(A,E) \tkzGetPoint{K}
	\tkzDefMidPoint(E,F) \tkzGetPoint{I}
	\tkzDefMidPoint(B,C) \tkzGetPoint{J}
	\tkzDrawPolygon[gray,fill=lightgray!15,line width=1pt](A,B,F,E)
	\tkzDrawPolygon[gray,fill=lightgray!15,line width=1pt](B,C,G,F)
	\tkzDrawPolygon[gray,fill=lightgray!15,line width=1pt](E,F,G,H)
	\tkzDrawSegment[gray,line width=1pt,dashed](A,D)
	\tkzDrawSegment[gray,line width=1pt,dashed](D,C)
	\tkzDrawSegment[gray,line width=1pt,dashed](H,D)
	\tkzDrawSegment[line width=1.5pt,densely dashed](K,H)
	\tkzDrawSegment[line width=1.5pt](A,I)
	\tkzDrawSegment[line width=1.5pt,densely dashed](I,J)
	\tkzDrawPoints[size=4](A,B,E,F,C,D,G,H,K,I,J)
	\tkzLabelPoints[left](A,E,K)
	\tkzLabelPoints[right](G,C)
	\tkzLabelPoints[above](F,H,I)
	\tkzLabelPoints[above right](D)
	\tkzLabelPoints[below right](B,J)
\end{tikzpicture}

\end{document}