quadrilateral orientation -4
\documentclass[tikz]{standalone}

\usepackage{pgflibraryshapes}
\usetikzlibrary{backgrounds}
\usetikzlibrary{arrows}
\begin{document}
\begin{tikzpicture}[scale = 0.5,font=\fontsize{8}{8}\selectfont]
\path (2.,2.) node(1_0) [draw,shape=circle,color=gray] {1};
\path (2.,-2.) node(2_0) [draw,shape=circle,color=gray] {2};
\path (-2.,-2.) node(3_0) [draw,shape=circle,color=gray] {3};
\path (-2.,2.) node(4_0) [draw,shape=circle,color=gray] {4};
\path
(2.,0.) node(5_0) [draw,shape=circle,color=gray] {5} --
(0.,-2.) node(6_0) [draw,shape=circle,color=gray] {6} --
(-2.,0.) node(7_0) [draw,shape=circle,color=gray] {7} --
(0.,2.) node(8_0) [draw,shape=circle,color=gray] {8} --
(0,0);
\draw[color=gray] (3_0) -- (6_0) -- (2_0) -- (5_0) -- (1_0) -- (8_0) -- (4_0) -- (7_0) -- (3_0);
\path (0.,0.) node(0_0) [] {};
\end{tikzpicture}
\end{document}
quadrilateral orientation -3
\documentclass[tikz]{standalone}

\usepackage{pgflibraryshapes}
\usetikzlibrary{backgrounds}
\usetikzlibrary{arrows}
\begin{document}
\begin{tikzpicture}[scale = 0.5,font=\fontsize{8}{8}\selectfont]
\path (2.,-2.) node(1_0) [draw,shape=circle,color=gray] {1};
\path (-2.,-2.) node(2_0) [draw,shape=circle,color=gray] {2};
\path (-2.,2.) node(3_0) [draw,shape=circle,color=gray] {3};
\path (2.,2.) node(4_0) [draw,shape=circle,color=gray] {4};
\path
(0.,-2.) node(5_0) [draw,shape=circle,color=gray] {5} --
(-2.,0.) node(6_0) [draw,shape=circle,color=gray] {6} --
(0.,2.) node(7_0) [draw,shape=circle,color=gray] {7} --
(2.,0.) node(8_0) [draw,shape=circle,color=gray] {8} --
(0,0);
\draw[color=gray] (2_0) -- (5_0) -- (1_0) -- (8_0) -- (4_0) -- (7_0) -- (3_0) -- (6_0) -- (2_0);
\path (0.,0.) node(0_0) [] {};
\end{tikzpicture}
\end{document}
quadrilateral orientation -2
\documentclass[tikz]{standalone}

\usepackage{pgflibraryshapes}
\usetikzlibrary{backgrounds}
\usetikzlibrary{arrows}
\begin{document}
\begin{tikzpicture}[scale = 0.5,font=\fontsize{8}{8}\selectfont]
\path (-2.,-2.) node(1_0) [draw,shape=circle,color=gray] {1};
\path (-2.,2.) node(2_0) [draw,shape=circle,color=gray] {2};
\path (2.,2.) node(3_0) [draw,shape=circle,color=gray] {3};
\path (2.,-2.) node(4_0) [draw,shape=circle,color=gray] {4};
\path
(-2.,0.) node(5_0) [draw,shape=circle,color=gray] {5} --
(0.,2.) node(6_0) [draw,shape=circle,color=gray] {6} --
(2.,0.) node(7_0) [draw,shape=circle,color=gray] {7} --
(0.,-2.) node(8_0) [draw,shape=circle,color=gray] {8} --
(0,0);
\draw[color=gray] (1_0) -- (8_0) -- (4_0) -- (7_0) -- (3_0) -- (6_0) -- (2_0) -- (5_0) -- (1_0);
\path (0.,0.) node(0_0) [] {};
\end{tikzpicture}
\end{document}
quadrilateral orientation -1
\documentclass[tikz]{standalone}

\usepackage{pgflibraryshapes}
\usetikzlibrary{backgrounds}
\usetikzlibrary{arrows}
\begin{document}
\begin{tikzpicture}[scale = 0.5,font=\fontsize{8}{8}\selectfont]
\path (-2.,2.) node(1_0) [draw,shape=circle,color=gray] {1};
\path (2.,2.) node(2_0) [draw,shape=circle,color=gray] {2};
\path (2.,-2.) node(3_0) [draw,shape=circle,color=gray] {3};
\path (-2.,-2.) node(4_0) [draw,shape=circle,color=gray] {4};
\path
(0.,2.) node(5_0) [draw,shape=circle,color=gray] {5} --
(2.,0.) node(6_0) [draw,shape=circle,color=gray] {6} --
(0.,-2.) node(7_0) [draw,shape=circle,color=gray] {7} --
(-2.,0.) node(8_0) [draw,shape=circle,color=gray] {8} --
(0,0);
\draw[color=gray] (4_0) -- (7_0) -- (3_0) -- (6_0) -- (2_0) -- (5_0) -- (1_0) -- (8_0) -- (4_0);
\path (0.,0.) node(0_0) [] {};
\end{tikzpicture}
\end{document}
quadrilateral orientation 0
\documentclass[tikz]{standalone}

\usepackage{pgflibraryshapes}
\usetikzlibrary{backgrounds}
\usetikzlibrary{arrows}
\begin{document}
\begin{tikzpicture}[scale = 0.5,font=\fontsize{8}{8}\selectfont]
\path (-2.,-2.) node(1_0) [draw,shape=circle,color=gray] {1};
\path (2.,-2.) node(2_0) [draw,shape=circle,color=gray] {2};
\path (2.,2.) node(3_0) [draw,shape=circle,color=gray] {3};
\path (-2.,2.) node(4_0) [draw,shape=circle,color=gray] {4};
\path
(0.,-2.) node(5_0) [draw,shape=circle,color=gray] {5} --
(2.,0.) node(6_0) [draw,shape=circle,color=gray] {6} --
(0.,2.) node(7_0) [draw,shape=circle,color=gray] {7} --
(-2.,0.) node(8_0) [draw,shape=circle,color=gray] {8} --
(0,0);
\draw[color=gray] (1_0) -- (5_0) -- (2_0) -- (6_0) -- (3_0) -- (7_0) -- (4_0) -- (8_0) -- (1_0);
\path (0.,0.) node(0_0) [] {};
\end{tikzpicture}
\end{document}
quadrilateral orientation 1
\documentclass[tikz]{standalone}

\usepackage{pgflibraryshapes}
\usetikzlibrary{backgrounds}
\usetikzlibrary{arrows}
\begin{document}
\begin{tikzpicture}[scale = 0.5,font=\fontsize{8}{8}\selectfont]
\path (-2.,2.) node(1_0) [draw,shape=circle,color=gray] {1};
\path (-2.,-2.) node(2_0) [draw,shape=circle,color=gray] {2};
\path (2.,-2.) node(3_0) [draw,shape=circle,color=gray] {3};
\path (2.,2.) node(4_0) [draw,shape=circle,color=gray] {4};
\path
(-2.,0.) node(5_0) [draw,shape=circle,color=gray] {5} --
(0.,-2.) node(6_0) [draw,shape=circle,color=gray] {6} --
(2.,0.) node(7_0) [draw,shape=circle,color=gray] {7} --
(0.,2.) node(8_0) [draw,shape=circle,color=gray] {8} --
(0,0);
\draw[color=gray] (2_0) -- (6_0) -- (3_0) -- (7_0) -- (4_0) -- (8_0) -- (1_0) -- (5_0) -- (2_0);
\path (0.,0.) node(0_0) [] {};
\end{tikzpicture}
\end{document}
quadrilateral orientation 2
\documentclass[tikz]{standalone}

\usepackage{pgflibraryshapes}
\usetikzlibrary{backgrounds}
\usetikzlibrary{arrows}
\begin{document}
\begin{tikzpicture}[scale = 0.5,font=\fontsize{8}{8}\selectfont]
\path (2.,2.) node(1_0) [draw,shape=circle,color=gray] {1};
\path (-2.,2.) node(2_0) [draw,shape=circle,color=gray] {2};
\path (-2.,-2.) node(3_0) [draw,shape=circle,color=gray] {3};
\path (2.,-2.) node(4_0) [draw,shape=circle,color=gray] {4};
\path
(0.,2.) node(5_0) [draw,shape=circle,color=gray] {5} --
(-2.,0.) node(6_0) [draw,shape=circle,color=gray] {6} --
(0.,-2.) node(7_0) [draw,shape=circle,color=gray] {7} --
(2.,0.) node(8_0) [draw,shape=circle,color=gray] {8} --
(0,0);
\draw[color=gray] (3_0) -- (7_0) -- (4_0) -- (8_0) -- (1_0) -- (5_0) -- (2_0) -- (6_0) -- (3_0);
\path (0.,0.) node(0_0) [] {};
\end{tikzpicture}
\end{document}
quadrilateral orientation 3
\documentclass[tikz]{standalone}

\usepackage{pgflibraryshapes}
\usetikzlibrary{backgrounds}
\usetikzlibrary{arrows}
\begin{document}
\begin{tikzpicture}[scale = 0.5,font=\fontsize{8}{8}\selectfont]
\path (2.,-2.) node(1_0) [draw,shape=circle,color=gray] {1};
\path (2.,2.) node(2_0) [draw,shape=circle,color=gray] {2};
\path (-2.,2.) node(3_0) [draw,shape=circle,color=gray] {3};
\path (-2.,-2.) node(4_0) [draw,shape=circle,color=gray] {4};
\path
(2.,0.) node(5_0) [draw,shape=circle,color=gray] {5} --
(0.,2.) node(6_0) [draw,shape=circle,color=gray] {6} --
(-2.,0.) node(7_0) [draw,shape=circle,color=gray] {7} --
(0.,-2.) node(8_0) [draw,shape=circle,color=gray] {8} --
(0,0);
\draw[color=gray] (4_0) -- (8_0) -- (1_0) -- (5_0) -- (2_0) -- (6_0) -- (3_0) -- (7_0) -- (4_0);
\path (0.,0.) node(0_0) [] {};
\end{tikzpicture}
\end{document}