\documentclass{article}
\thispagestyle{empty}
\usepackage{tikz}
\usetikzlibrary{calc}
\begin{document}
\begin{tikzpicture}[node distance=2.5cm,semithick]
\tikzstyle{origVertex} = [draw, blue, fill, shape=circle]
\tikzstyle{dualVertex} = [draw, red, fill, shape=circle]
\tikzstyle{invisibleVertex} = [shape=circle]
\tikzstyle{origEdge} = [blue]
\tikzstyle{dualEdge} = [red, densely dashed]
\node[origVertex] (0) {};
\node[invisibleVertex] (i1) [right of=0] {};
\node[origVertex] (1) [right of=i1] {};
\node[origVertex] (2) [below right of=1] {};
\node[origVertex] (3) [below left of=2] {};
\node[invisibleVertex] (i2) [left of=3] {};
\node[origVertex] (4) [left of=i2] {};
\path (0) edge[origEdge] (1)
edge[origEdge] (4)
(1) edge[origEdge] (2)
edge[origEdge] (3)
edge[origEdge] (4)
(2) edge[origEdge] (3)
(3) edge[origEdge] (4);
\path let
\p1 = (0),
\p2 = (1),
\p3 = (4)
in
node[dualVertex] (d0) at (\x1/3+\x2/3+\x3/3,\y1/3+\y2/3+\y3/3) {};
\path let
\p1 = (1),
\p2 = (3),
\p3 = (4)
in
node[dualVertex] (d1) at (\x1/3+\x2/3+\x3/3,\y1/3+\y2/3+\y3/3) {};
\path let
\p1 = (1),
\p2 = (2),
\p3 = (3)
in
node[dualVertex] (d2) at (\x1/3+\x2/3+\x3/3,\y1/3+\y2/3+\y3/3) {};
\node[dualVertex] (d3) [below left of=3] {};
\path (d0) edge[dualEdge] (d1)
edge[dualEdge, out= 120, in=-170, looseness=4] (d3)
edge[dualEdge, out=-150, in= 170, looseness=2.5] (d3)
(d1) edge[dualEdge] (d2)
edge[dualEdge] (d3)
(d2) edge[dualEdge, out= 35, in= 0, looseness=2] (d3)
edge[dualEdge, out= -90, in= 20, looseness=1.5] (d3);
\end{tikzpicture}
\end{document}