\documentclass[11pt]{report}
\input{header}
\pagestyle{empty}
\begin{document}
\psscalebox{1.8}{\arrset{0.9}
  \pspicture[](-1,-1)(8,8)
  \arraxes(0,0)(-1,-1)(8,8)
  %
  \pspolygon[fillstyle=vlines,hatchcolor=mediumred,hatchwidth=0.25pt,hatchsep=2pt](1,4)(4,1)(7,4)(4,7)
  \pspolygon[fillstyle=hlines,hatchcolor=mediumblue,hatchwidth=0.25pt,hatchsep=2pt](2,2)(6,2)(6,6)(2,6)
  %
  \arrMainVertex(1,4){a1}
  \arrMainVertex(4,1){a2}
  \arrMainVertex(7,4){a3}
  \arrMainVertex(4,7){a4}
  \arrBlueVertex(2,2){b1}
  \arrBlueVertex(6,2){b2}
  \arrBlueVertex(6,6){b3}
  \arrBlueVertex(2,6){b4}
  \arrEmptyVertex(2,3){x1}
  \arrEmptyVertex(3,2){x2}
  \arrEmptyVertex(5,2){x3}
  \arrEmptyVertex(6,3){x4}
  \arrEmptyVertex(6,5){x5}
  \arrEmptyVertex(5,6){x6}
  \arrEmptyVertex(3,6){x7}
  \arrEmptyVertex(2,5){x8}
  %
  \ncline[linewidth=1pt,linecolor=blue]{b1}{x2}
  \ncline[linewidth=1pt,linecolor=blue]{x2}{x3}
  \ncline[linewidth=1pt,linecolor=blue]{x3}{b2}
  \ncline[linewidth=1pt,linecolor=blue]{b2}{x4}
  \ncline[linewidth=1pt,linecolor=blue]{x4}{x5}
  \ncline[linewidth=1pt,linecolor=blue]{x5}{b3}
  \ncline[linewidth=1pt,linecolor=blue]{b3}{x6}
  \ncline[linewidth=1pt,linecolor=blue]{x6}{x7}
  \ncline[linewidth=1pt,linecolor=blue]{x7}{b4}
  \ncline[linewidth=1pt,linecolor=blue]{b4}{x8}
  \ncline[linewidth=1pt,linecolor=blue]{x8}{x1}
  \ncline[linewidth=1pt,linecolor=blue]{x1}{b1}
  %
  \ncline[linewidth=1pt,linecolor=red]{a1}{x1}
  \ncline[linewidth=1pt,linecolor=red]{x1}{x2}
  \ncline[linewidth=1pt,linecolor=red]{x2}{a2}
  \ncline[linewidth=1pt,linecolor=red]{a2}{x3}
  \ncline[linewidth=1pt,linecolor=red]{x3}{x4}
  \ncline[linewidth=1pt,linecolor=red]{x4}{a3}
  \ncline[linewidth=1pt,linecolor=red]{a3}{x5}
  \ncline[linewidth=1pt,linecolor=red]{x5}{x6}
  \ncline[linewidth=1pt,linecolor=red]{x6}{a4}
  \ncline[linewidth=1pt,linecolor=red]{a4}{x7}
  \ncline[linewidth=1pt,linecolor=red]{x7}{x8}
  \ncline[linewidth=1pt,linecolor=red]{x8}{a1}
  \rput(4,4){\boldmath{$\hat{f}$}}
  \endpspicture
}
\end{document}
