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

\usepackage{pgflibraryshapes}
\usetikzlibrary{backgrounds}
\usetikzlibrary{arrows}
\begin{document}
\begin{tikzpicture}[scale = 1.,font=\fontsize{8}{8}\selectfont]
\path (0.,0.) node(4_0) [draw,shape=circle,color=gray] {4};
\path (2.,2.) node(5_0) [draw,shape=circle,color=gray] {5};
\path (2.,-2.) node(6_0) [draw,shape=circle,color=gray] {6};
\path (-2.,-2.) node(7_0) [draw,shape=circle,color=gray] {7};
\path (-2.,2.) node(8_0) [draw,shape=circle,color=gray] {8};
\path (2.,0.) node(9_0) [draw,shape=circle,color=gray] {9};
\path (0.,-2.) node(10_0) [draw,shape=circle,color=gray] {10};
\path (-2.,0.) node(11_0) [draw,shape=circle,color=gray] {11};
\path (0.,2.) node(12_0) [draw,shape=circle,color=gray] {12};
\path
(0.,-1.) node(13_0) [draw,shape=circle,color=gray] {13} --
(1.,0.) node(14_0) [draw,shape=circle,color=gray] {14} --
(0.,1.) node(15_0) [draw,shape=circle,color=gray] {15} --
(-1.,0.) node(16_0) [draw,shape=circle,color=gray] {16} --
(2.,1.) node(17_0) [draw,shape=circle,color=gray] {17} --
(2.,-1.) node(18_0) [draw,shape=circle,color=gray] {18} --
(1.,-2.) node(19_0) [draw,shape=circle,color=gray] {19} --
(-1.,-2.) node(20_0) [draw,shape=circle,color=gray] {20} --
(-2.,-1.) node(21_0) [draw,shape=circle,color=gray] {21} --
(-2.,1.) node(22_0) [draw,shape=circle,color=gray] {22} --
(-1.,2.) node(23_0) [draw,shape=circle,color=gray] {23} --
(1.,2.) node(24_0) [draw,shape=circle,color=gray] {24} --
(0,0);
\draw[color=gray] (7_0) -- (20_0) -- (10_0) -- (13_0) -- (4_0) -- (16_0) -- (11_0) -- (21_0) -- (7_0);
\draw[color=gray] (10_0) -- (19_0) -- (6_0) -- (18_0) -- (9_0) -- (14_0) -- (4_0) -- (13_0) -- (10_0);
\draw[color=gray] (4_0) -- (14_0) -- (9_0) -- (17_0) -- (5_0) -- (24_0) -- (12_0) -- (15_0) -- (4_0);
\draw[color=gray] (11_0) -- (16_0) -- (4_0) -- (15_0) -- (12_0) -- (23_0) -- (8_0) -- (22_0) -- (11_0);
\path (-1.,-1.) node(0_0) [] {};
\path (1.,-1.) node(1_0) [] {};
\path (1.,1.) node(2_0) [] {};
\path (-1.,1.) node(3_0) [] {};
\end{tikzpicture}
\end{document}
quadrilateral orientation -3
\documentclass[tikz]{standalone}

\usepackage{pgflibraryshapes}
\usetikzlibrary{backgrounds}
\usetikzlibrary{arrows}
\begin{document}
\begin{tikzpicture}[scale = 1.,font=\fontsize{8}{8}\selectfont]
\path (0.,0.) node(4_0) [draw,shape=circle,color=gray] {4};
\path (2.,-2.) node(5_0) [draw,shape=circle,color=gray] {5};
\path (-2.,-2.) node(6_0) [draw,shape=circle,color=gray] {6};
\path (-2.,2.) node(7_0) [draw,shape=circle,color=gray] {7};
\path (2.,2.) node(8_0) [draw,shape=circle,color=gray] {8};
\path (0.,-2.) node(9_0) [draw,shape=circle,color=gray] {9};
\path (-2.,0.) node(10_0) [draw,shape=circle,color=gray] {10};
\path (0.,2.) node(11_0) [draw,shape=circle,color=gray] {11};
\path (2.,0.) node(12_0) [draw,shape=circle,color=gray] {12};
\path
(0.,-1.) node(13_0) [draw,shape=circle,color=gray] {13} --
(1.,0.) node(14_0) [draw,shape=circle,color=gray] {14} --
(0.,1.) node(15_0) [draw,shape=circle,color=gray] {15} --
(-1.,0.) node(16_0) [draw,shape=circle,color=gray] {16} --
(1.,-2.) node(17_0) [draw,shape=circle,color=gray] {17} --
(-1.,-2.) node(18_0) [draw,shape=circle,color=gray] {18} --
(-2.,-1.) node(19_0) [draw,shape=circle,color=gray] {19} --
(-2.,1.) node(20_0) [draw,shape=circle,color=gray] {20} --
(-1.,2.) node(21_0) [draw,shape=circle,color=gray] {21} --
(1.,2.) node(22_0) [draw,shape=circle,color=gray] {22} --
(2.,1.) node(23_0) [draw,shape=circle,color=gray] {23} --
(2.,-1.) node(24_0) [draw,shape=circle,color=gray] {24} --
(0,0);
\draw[color=gray] (6_0) -- (18_0) -- (9_0) -- (13_0) -- (4_0) -- (16_0) -- (10_0) -- (19_0) -- (6_0);
\draw[color=gray] (9_0) -- (17_0) -- (5_0) -- (24_0) -- (12_0) -- (14_0) -- (4_0) -- (13_0) -- (9_0);
\draw[color=gray] (4_0) -- (14_0) -- (12_0) -- (23_0) -- (8_0) -- (22_0) -- (11_0) -- (15_0) -- (4_0);
\draw[color=gray] (10_0) -- (16_0) -- (4_0) -- (15_0) -- (11_0) -- (21_0) -- (7_0) -- (20_0) -- (10_0);
\path (-1.,-1.) node(0_0) [] {};
\path (1.,-1.) node(1_0) [] {};
\path (1.,1.) node(2_0) [] {};
\path (-1.,1.) node(3_0) [] {};
\end{tikzpicture}
\end{document}
quadrilateral orientation -2
\documentclass[tikz]{standalone}

\usepackage{pgflibraryshapes}
\usetikzlibrary{backgrounds}
\usetikzlibrary{arrows}
\begin{document}
\begin{tikzpicture}[scale = 1.,font=\fontsize{8}{8}\selectfont]
\path (0.,0.) node(4_0) [draw,shape=circle,color=gray] {4};
\path (-2.,-2.) node(5_0) [draw,shape=circle,color=gray] {5};
\path (-2.,2.) node(6_0) [draw,shape=circle,color=gray] {6};
\path (2.,2.) node(7_0) [draw,shape=circle,color=gray] {7};
\path (2.,-2.) node(8_0) [draw,shape=circle,color=gray] {8};
\path (-2.,0.) node(9_0) [draw,shape=circle,color=gray] {9};
\path (0.,2.) node(10_0) [draw,shape=circle,color=gray] {10};
\path (2.,0.) node(11_0) [draw,shape=circle,color=gray] {11};
\path (0.,-2.) node(12_0) [draw,shape=circle,color=gray] {12};
\path
(0.,-1.) node(13_0) [draw,shape=circle,color=gray] {13} --
(1.,0.) node(14_0) [draw,shape=circle,color=gray] {14} --
(0.,1.) node(15_0) [draw,shape=circle,color=gray] {15} --
(-1.,0.) node(16_0) [draw,shape=circle,color=gray] {16} --
(-2.,-1.) node(17_0) [draw,shape=circle,color=gray] {17} --
(-2.,1.) node(18_0) [draw,shape=circle,color=gray] {18} --
(-1.,2.) node(19_0) [draw,shape=circle,color=gray] {19} --
(1.,2.) node(20_0) [draw,shape=circle,color=gray] {20} --
(2.,1.) node(21_0) [draw,shape=circle,color=gray] {21} --
(2.,-1.) node(22_0) [draw,shape=circle,color=gray] {22} --
(1.,-2.) node(23_0) [draw,shape=circle,color=gray] {23} --
(-1.,-2.) node(24_0) [draw,shape=circle,color=gray] {24} --
(0,0);
\draw[color=gray] (5_0) -- (24_0) -- (12_0) -- (13_0) -- (4_0) -- (16_0) -- (9_0) -- (17_0) -- (5_0);
\draw[color=gray] (12_0) -- (23_0) -- (8_0) -- (22_0) -- (11_0) -- (14_0) -- (4_0) -- (13_0) -- (12_0);
\draw[color=gray] (4_0) -- (14_0) -- (11_0) -- (21_0) -- (7_0) -- (20_0) -- (10_0) -- (15_0) -- (4_0);
\draw[color=gray] (9_0) -- (16_0) -- (4_0) -- (15_0) -- (10_0) -- (19_0) -- (6_0) -- (18_0) -- (9_0);
\path (-1.,-1.) node(0_0) [] {};
\path (1.,-1.) node(1_0) [] {};
\path (1.,1.) node(2_0) [] {};
\path (-1.,1.) node(3_0) [] {};
\end{tikzpicture}
\end{document}
quadrilateral orientation -1
\documentclass[tikz]{standalone}

\usepackage{pgflibraryshapes}
\usetikzlibrary{backgrounds}
\usetikzlibrary{arrows}
\begin{document}
\begin{tikzpicture}[scale = 1.,font=\fontsize{8}{8}\selectfont]
\path (0.,0.) node(4_0) [draw,shape=circle,color=gray] {4};
\path (-2.,2.) node(5_0) [draw,shape=circle,color=gray] {5};
\path (2.,2.) node(6_0) [draw,shape=circle,color=gray] {6};
\path (2.,-2.) node(7_0) [draw,shape=circle,color=gray] {7};
\path (-2.,-2.) node(8_0) [draw,shape=circle,color=gray] {8};
\path (0.,2.) node(9_0) [draw,shape=circle,color=gray] {9};
\path (2.,0.) node(10_0) [draw,shape=circle,color=gray] {10};
\path (0.,-2.) node(11_0) [draw,shape=circle,color=gray] {11};
\path (-2.,0.) node(12_0) [draw,shape=circle,color=gray] {12};
\path
(0.,-1.) node(13_0) [draw,shape=circle,color=gray] {13} --
(1.,0.) node(14_0) [draw,shape=circle,color=gray] {14} --
(0.,1.) node(15_0) [draw,shape=circle,color=gray] {15} --
(-1.,0.) node(16_0) [draw,shape=circle,color=gray] {16} --
(-1.,2.) node(17_0) [draw,shape=circle,color=gray] {17} --
(1.,2.) node(18_0) [draw,shape=circle,color=gray] {18} --
(2.,1.) node(19_0) [draw,shape=circle,color=gray] {19} --
(2.,-1.) node(20_0) [draw,shape=circle,color=gray] {20} --
(1.,-2.) node(21_0) [draw,shape=circle,color=gray] {21} --
(-1.,-2.) node(22_0) [draw,shape=circle,color=gray] {22} --
(-2.,-1.) node(23_0) [draw,shape=circle,color=gray] {23} --
(-2.,1.) node(24_0) [draw,shape=circle,color=gray] {24} --
(0,0);
\draw[color=gray] (8_0) -- (22_0) -- (11_0) -- (13_0) -- (4_0) -- (16_0) -- (12_0) -- (23_0) -- (8_0);
\draw[color=gray] (11_0) -- (21_0) -- (7_0) -- (20_0) -- (10_0) -- (14_0) -- (4_0) -- (13_0) -- (11_0);
\draw[color=gray] (4_0) -- (14_0) -- (10_0) -- (19_0) -- (6_0) -- (18_0) -- (9_0) -- (15_0) -- (4_0);
\draw[color=gray] (12_0) -- (16_0) -- (4_0) -- (15_0) -- (9_0) -- (17_0) -- (5_0) -- (24_0) -- (12_0);
\path (-1.,-1.) node(0_0) [] {};
\path (1.,-1.) node(1_0) [] {};
\path (1.,1.) node(2_0) [] {};
\path (-1.,1.) node(3_0) [] {};
\end{tikzpicture}
\end{document}
quadrilateral orientation 0
\documentclass[tikz]{standalone}

\usepackage{pgflibraryshapes}
\usetikzlibrary{backgrounds}
\usetikzlibrary{arrows}
\begin{document}
\begin{tikzpicture}[scale = 1.,font=\fontsize{8}{8}\selectfont]
\path (0.,0.) node(4_0) [draw,shape=circle,color=gray] {4};
\path (-2.,-2.) node(5_0) [draw,shape=circle,color=gray] {5};
\path (2.,-2.) node(6_0) [draw,shape=circle,color=gray] {6};
\path (2.,2.) node(7_0) [draw,shape=circle,color=gray] {7};
\path (-2.,2.) node(8_0) [draw,shape=circle,color=gray] {8};
\path (0.,-2.) node(9_0) [draw,shape=circle,color=gray] {9};
\path (2.,0.) node(10_0) [draw,shape=circle,color=gray] {10};
\path (0.,2.) node(11_0) [draw,shape=circle,color=gray] {11};
\path (-2.,0.) node(12_0) [draw,shape=circle,color=gray] {12};
\path
(0.,-1.) node(13_0) [draw,shape=circle,color=gray] {13} --
(1.,0.) node(14_0) [draw,shape=circle,color=gray] {14} --
(0.,1.) node(15_0) [draw,shape=circle,color=gray] {15} --
(-1.,0.) node(16_0) [draw,shape=circle,color=gray] {16} --
(-1.,-2.) node(17_0) [draw,shape=circle,color=gray] {17} --
(1.,-2.) node(18_0) [draw,shape=circle,color=gray] {18} --
(2.,-1.) node(19_0) [draw,shape=circle,color=gray] {19} --
(2.,1.) node(20_0) [draw,shape=circle,color=gray] {20} --
(1.,2.) node(21_0) [draw,shape=circle,color=gray] {21} --
(-1.,2.) node(22_0) [draw,shape=circle,color=gray] {22} --
(-2.,1.) node(23_0) [draw,shape=circle,color=gray] {23} --
(-2.,-1.) node(24_0) [draw,shape=circle,color=gray] {24} --
(0,0);
\draw[color=gray] (5_0) -- (17_0) -- (9_0) -- (13_0) -- (4_0) -- (16_0) -- (12_0) -- (24_0) -- (5_0);
\draw[color=gray] (9_0) -- (18_0) -- (6_0) -- (19_0) -- (10_0) -- (14_0) -- (4_0) -- (13_0) -- (9_0);
\draw[color=gray] (4_0) -- (14_0) -- (10_0) -- (20_0) -- (7_0) -- (21_0) -- (11_0) -- (15_0) -- (4_0);
\draw[color=gray] (12_0) -- (16_0) -- (4_0) -- (15_0) -- (11_0) -- (22_0) -- (8_0) -- (23_0) -- (12_0);
\path (-1.,-1.) node(0_0) [] {};
\path (1.,-1.) node(1_0) [] {};
\path (1.,1.) node(2_0) [] {};
\path (-1.,1.) node(3_0) [] {};
\end{tikzpicture}
\end{document}
quadrilateral orientation 1
\documentclass[tikz]{standalone}

\usepackage{pgflibraryshapes}
\usetikzlibrary{backgrounds}
\usetikzlibrary{arrows}
\begin{document}
\begin{tikzpicture}[scale = 1.,font=\fontsize{8}{8}\selectfont]
\path (0.,0.) node(4_0) [draw,shape=circle,color=gray] {4};
\path (-2.,2.) node(5_0) [draw,shape=circle,color=gray] {5};
\path (-2.,-2.) node(6_0) [draw,shape=circle,color=gray] {6};
\path (2.,-2.) node(7_0) [draw,shape=circle,color=gray] {7};
\path (2.,2.) node(8_0) [draw,shape=circle,color=gray] {8};
\path (-2.,0.) node(9_0) [draw,shape=circle,color=gray] {9};
\path (0.,-2.) node(10_0) [draw,shape=circle,color=gray] {10};
\path (2.,0.) node(11_0) [draw,shape=circle,color=gray] {11};
\path (0.,2.) node(12_0) [draw,shape=circle,color=gray] {12};
\path
(0.,-1.) node(13_0) [draw,shape=circle,color=gray] {13} --
(1.,0.) node(14_0) [draw,shape=circle,color=gray] {14} --
(0.,1.) node(15_0) [draw,shape=circle,color=gray] {15} --
(-1.,0.) node(16_0) [draw,shape=circle,color=gray] {16} --
(-2.,1.) node(17_0) [draw,shape=circle,color=gray] {17} --
(-2.,-1.) node(18_0) [draw,shape=circle,color=gray] {18} --
(-1.,-2.) node(19_0) [draw,shape=circle,color=gray] {19} --
(1.,-2.) node(20_0) [draw,shape=circle,color=gray] {20} --
(2.,-1.) node(21_0) [draw,shape=circle,color=gray] {21} --
(2.,1.) node(22_0) [draw,shape=circle,color=gray] {22} --
(1.,2.) node(23_0) [draw,shape=circle,color=gray] {23} --
(-1.,2.) node(24_0) [draw,shape=circle,color=gray] {24} --
(0,0);
\draw[color=gray] (6_0) -- (19_0) -- (10_0) -- (13_0) -- (4_0) -- (16_0) -- (9_0) -- (18_0) -- (6_0);
\draw[color=gray] (10_0) -- (20_0) -- (7_0) -- (21_0) -- (11_0) -- (14_0) -- (4_0) -- (13_0) -- (10_0);
\draw[color=gray] (4_0) -- (14_0) -- (11_0) -- (22_0) -- (8_0) -- (23_0) -- (12_0) -- (15_0) -- (4_0);
\draw[color=gray] (9_0) -- (16_0) -- (4_0) -- (15_0) -- (12_0) -- (24_0) -- (5_0) -- (17_0) -- (9_0);
\path (-1.,-1.) node(0_0) [] {};
\path (1.,-1.) node(1_0) [] {};
\path (1.,1.) node(2_0) [] {};
\path (-1.,1.) node(3_0) [] {};
\end{tikzpicture}
\end{document}
quadrilateral orientation 2
\documentclass[tikz]{standalone}

\usepackage{pgflibraryshapes}
\usetikzlibrary{backgrounds}
\usetikzlibrary{arrows}
\begin{document}
\begin{tikzpicture}[scale = 1.,font=\fontsize{8}{8}\selectfont]
\path (0.,0.) node(4_0) [draw,shape=circle,color=gray] {4};
\path (2.,2.) node(5_0) [draw,shape=circle,color=gray] {5};
\path (-2.,2.) node(6_0) [draw,shape=circle,color=gray] {6};
\path (-2.,-2.) node(7_0) [draw,shape=circle,color=gray] {7};
\path (2.,-2.) node(8_0) [draw,shape=circle,color=gray] {8};
\path (0.,2.) node(9_0) [draw,shape=circle,color=gray] {9};
\path (-2.,0.) node(10_0) [draw,shape=circle,color=gray] {10};
\path (0.,-2.) node(11_0) [draw,shape=circle,color=gray] {11};
\path (2.,0.) node(12_0) [draw,shape=circle,color=gray] {12};
\path
(0.,-1.) node(13_0) [draw,shape=circle,color=gray] {13} --
(1.,0.) node(14_0) [draw,shape=circle,color=gray] {14} --
(0.,1.) node(15_0) [draw,shape=circle,color=gray] {15} --
(-1.,0.) node(16_0) [draw,shape=circle,color=gray] {16} --
(1.,2.) node(17_0) [draw,shape=circle,color=gray] {17} --
(-1.,2.) node(18_0) [draw,shape=circle,color=gray] {18} --
(-2.,1.) node(19_0) [draw,shape=circle,color=gray] {19} --
(-2.,-1.) node(20_0) [draw,shape=circle,color=gray] {20} --
(-1.,-2.) node(21_0) [draw,shape=circle,color=gray] {21} --
(1.,-2.) node(22_0) [draw,shape=circle,color=gray] {22} --
(2.,-1.) node(23_0) [draw,shape=circle,color=gray] {23} --
(2.,1.) node(24_0) [draw,shape=circle,color=gray] {24} --
(0,0);
\draw[color=gray] (7_0) -- (21_0) -- (11_0) -- (13_0) -- (4_0) -- (16_0) -- (10_0) -- (20_0) -- (7_0);
\draw[color=gray] (11_0) -- (22_0) -- (8_0) -- (23_0) -- (12_0) -- (14_0) -- (4_0) -- (13_0) -- (11_0);
\draw[color=gray] (4_0) -- (14_0) -- (12_0) -- (24_0) -- (5_0) -- (17_0) -- (9_0) -- (15_0) -- (4_0);
\draw[color=gray] (10_0) -- (16_0) -- (4_0) -- (15_0) -- (9_0) -- (18_0) -- (6_0) -- (19_0) -- (10_0);
\path (-1.,-1.) node(0_0) [] {};
\path (1.,-1.) node(1_0) [] {};
\path (1.,1.) node(2_0) [] {};
\path (-1.,1.) node(3_0) [] {};
\end{tikzpicture}
\end{document}
quadrilateral orientation 3
\documentclass[tikz]{standalone}

\usepackage{pgflibraryshapes}
\usetikzlibrary{backgrounds}
\usetikzlibrary{arrows}
\begin{document}
\begin{tikzpicture}[scale = 1.,font=\fontsize{8}{8}\selectfont]
\path (0.,0.) node(4_0) [draw,shape=circle,color=gray] {4};
\path (2.,-2.) node(5_0) [draw,shape=circle,color=gray] {5};
\path (2.,2.) node(6_0) [draw,shape=circle,color=gray] {6};
\path (-2.,2.) node(7_0) [draw,shape=circle,color=gray] {7};
\path (-2.,-2.) node(8_0) [draw,shape=circle,color=gray] {8};
\path (2.,0.) node(9_0) [draw,shape=circle,color=gray] {9};
\path (0.,2.) node(10_0) [draw,shape=circle,color=gray] {10};
\path (-2.,0.) node(11_0) [draw,shape=circle,color=gray] {11};
\path (0.,-2.) node(12_0) [draw,shape=circle,color=gray] {12};
\path
(0.,-1.) node(13_0) [draw,shape=circle,color=gray] {13} --
(1.,0.) node(14_0) [draw,shape=circle,color=gray] {14} --
(0.,1.) node(15_0) [draw,shape=circle,color=gray] {15} --
(-1.,0.) node(16_0) [draw,shape=circle,color=gray] {16} --
(2.,-1.) node(17_0) [draw,shape=circle,color=gray] {17} --
(2.,1.) node(18_0) [draw,shape=circle,color=gray] {18} --
(1.,2.) node(19_0) [draw,shape=circle,color=gray] {19} --
(-1.,2.) node(20_0) [draw,shape=circle,color=gray] {20} --
(-2.,1.) node(21_0) [draw,shape=circle,color=gray] {21} --
(-2.,-1.) node(22_0) [draw,shape=circle,color=gray] {22} --
(-1.,-2.) node(23_0) [draw,shape=circle,color=gray] {23} --
(1.,-2.) node(24_0) [draw,shape=circle,color=gray] {24} --
(0,0);
\draw[color=gray] (8_0) -- (23_0) -- (12_0) -- (13_0) -- (4_0) -- (16_0) -- (11_0) -- (22_0) -- (8_0);
\draw[color=gray] (12_0) -- (24_0) -- (5_0) -- (17_0) -- (9_0) -- (14_0) -- (4_0) -- (13_0) -- (12_0);
\draw[color=gray] (4_0) -- (14_0) -- (9_0) -- (18_0) -- (6_0) -- (19_0) -- (10_0) -- (15_0) -- (4_0);
\draw[color=gray] (11_0) -- (16_0) -- (4_0) -- (15_0) -- (10_0) -- (20_0) -- (7_0) -- (21_0) -- (11_0);
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\end{document}