\documentclass{book}

\usepackage{tikz}
\usetikzlibrary{shadows,shapes,arrows,chains,decorations.pathreplacing,calc}
\usepackage{amsthm,amssymb,amsmath,tikz}
\tikzstyle{vertex}=[circle, draw, sep=0pt, minimum size=0.001 pt] 
\newcommand{\vertex}{\node[vertex]}
\begin{document}

\begin{figure}[!ht]
\centering
 \begin{tikzpicture} 
\vertex (1) at (0,0)[label=above:$A$]{};
\vertex (2) at (-1.5,-3) [label=above:$B$]{};

\vertex (3) at (1.5,-3) [label=above:$C$]{};
\vertex (4) at (6,-3) [label=above:$D$]{};
\vertex (5) at (-3,-6) [label=below:]{};
\vertex (6) at (-0.5,-6) [label=above:]{};
\vertex (7) at (0.5,-6) [label=above:]{};
\vertex (8) at (3,-6) [label=above:]{};
\vertex (9) at (5,-6) [label=below:]{};
\vertex (10) at (8,-6) [label=above:]{};
\draw (3)  [dashed] edge (4);
\draw (1)   edge (2);
\draw (1)   edge (3);
\draw (1)   edge (4);
\draw (2)   edge (5);
\draw (3)   edge (7);
\draw (3)   edge (8);
\draw (7)   edge (8);
\draw (4)   edge (9);
\draw (4)   edge (10);
\draw (9)   edge (10);
\draw (5)   edge (6);
\draw (2)   edge (6);

\end{tikzpicture}
\caption{}
\label{sh4}
\end{figure}

\end{document}