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\documentclass[tikz,11pt]{standalone}
\usepackage{tikz}
\usepackage{tikz-3dplot}
\usetikzlibrary{arrows.meta}
\pgfmathsetmacro{\polytopeLineWidth}{1.2pt}
\pgfmathsetmacro{\dotSize}{0.5mm}
\definecolor{fillColor}{rgb}{0.8,0.8,0.8}
\pgfmathsetmacro{\opacity}{0.7}
\pgfmathsetmacro{\rotation}{72}
\pgfmathsetmacro{\zRotation}{30}
% \pgfmathsetmacro{\rotation}{100}
% \pgfmathsetmacro{\zRotation}{30}
\newcommand{\point}[1]{
\path (#1) node[fill, black, circle, inner sep=\dotSize] {};
}
\begin{document}
\begin{tikzpicture}[line join=bevel, line width=\polytopeLineWidth, scale=1.1]
\begin{scope}
\path [draw, -Stealth] (1.7, 2.4) -- node [above] {dual} (3.7, 2.4);
\path [draw, -Stealth] (5, -0.5) -- node [right] {convex hull} (5, -1.5);
\node at (0, 0) {$\nabla$};
\tdplotsetmaincoords{\rotation}{-\zRotation}
\tdplotsetrotatedcoords{0}{90}{90}
% \begin{tikzpicture}[tdplot_main_coords]
% \draw[thick,->] (0,0,0) -- (1,0,0) node[anchor=north east]{$x$};
% \draw[thick,->] (0,0,0) -- (0,1,0) node[anchor=north west]{$y$};
% \draw[thick,->] (0,0,0) -- (0,0,1) node[anchor=south]{$z$};
% \end{tikzpicture}
\begin{scope}[tdplot_rotated_coords, xshift=0.2cm, yshift=3.4cm]
% back faces
\path [draw, fill opacity=\opacity, fill=fillColor] (2.,0.,-1.)--(0.,0.,1.)--(-3.,-2.,-1.)--cycle;
\path [draw, fill opacity=\opacity, fill=fillColor] (0.,1.,0.)--(0.,0.,1.)--(2.,0.,-1.)--cycle;
% back points
\point{1,0,0};
\point{0.,0.,0.}; % inside
% front faces
\path [draw, fill opacity=\opacity, fill=fillColor] (0.,1.,0.)--(2.,0.,-1.)--(-3.,-2.,-1.)--cycle;
\path [draw, fill opacity=\opacity, fill=fillColor] (0.,0.,1.)--(0.,1.,0.)--(-3.,-2.,-1.)--cycle;
% front points
\point{2.,0.,-1.};
\point{0.,1.,0.};
\point{0.,0.,1.};
\point{-3.,-2.,-1.};
\end{scope}
\end{scope}
% \begin{scope}
% \path [draw, -Stealth] (1.7, 2.4) --(3.7, 2.4);
% \path [draw, -Stealth] (5, -0.5) --(5, -1.5);
% \node at (0, 0) {$\nabla$};
% \tdplotsetmaincoords{\rotation}{180 - \zRotation}
% \tdplotsetrotatedcoords{0}{90}{90}
% \begin{scope}[tdplot_rotated_coords, xshift=0.2cm, yshift=3.4cm]
% % \begin{scope}[tdplot_rotated_coords]
% % \draw[thick,->] (0,0,0) -- (1,0,0) node[anchor=north east]{$x$};
% % \draw[thick,->] (0,0,0) -- (0,1,0) node[anchor=north west]{$y$};
% % \draw[thick,->] (0,0,0) -- (0,0,1) node[anchor=south]{$z$};
% % \end{scope}
% % back faces
% \path [draw, fill opacity=\opacity, fill=fillColor] (0.,1.,0.)--(2.,0.,-1.)--(-3.,-2.,-1.)--cycle;
% \path [draw, fill opacity=\opacity, fill=fillColor] (0.,0.,1.)--(0.,1.,0.)--(-3.,-2.,-1.)--cycle;
% % back points
% \point{2.,0.,-1.};
% \point{0.,1.,0.};
% \point{0.,0.,1.};
% \point{-3.,-2.,-1.};
% \point{0.,0.,0.}; % inside
% % front faces
% \path [draw, fill opacity=\opacity, fill=fillColor] (2.,0.,-1.)--(0.,0.,1.)--(-3.,-2.,-1.)--cycle;
% \path [draw, fill opacity=\opacity, fill=fillColor] (0.,1.,0.)--(0.,0.,1.)--(2.,0.,-1.)--cycle;
% % front points
% \point{1,0,0};
% \end{scope}
% \end{scope}
\begin{scope}[xshift=5cm]
\node at (0, 0) {$\nabla^*$};
\tdplotsetmaincoords{\rotation}{180 - \zRotation}
\tdplotsetrotatedcoords{0}{90}{90}
\begin{scope}[tdplot_rotated_coords, yshift=1.8cm]
% back faces
\path [draw, fill opacity=0.7, fill=fillColor] (1.333,-1.,-1.)--(-1.,-1.,-1.)--(-1.,2.5,-1.)--cycle;
\path [draw, fill opacity=0.7, fill=fillColor] (-1.,-1.,-1.)--(0.4,-1.,1.8)--(-1.,2.5,-1.)--cycle;
\path [draw, fill opacity=0.7, fill=fillColor] (0.4,-1.,1.8)--(-1.,-1.,-1.)--(1.333,-1.,-1.)--cycle;
% back points
\point{-1.,-1.,-1.};
\point{0.,-1.,-1.};
\point{1.,-1.,-1.};
\point{-1.,0.,-1.};
\point{-1.,1.,-1.};
\point{-1.,2.,-1.};
\point{0.,-1.,1.};
\point{0.,0.,-1.}; % on face
\point{0.,-1.,0.}; % on face
\point{0.,0.,0.}; % inside
% front faces
\path [draw, fill opacity=0.7, fill=fillColor] (0.4,-1.,1.8)--(1.333,-1.,-1.)--(-1.,2.5,-1.)--cycle;
% front points
\point{0.,1.,-1.};
\point{0.,0.,1.};
\point{1.,-1.,0.};
\end{scope}
\end{scope}
\begin{scope}[xshift=5cm, yshift=-6.5cm]
\node at (0, 0) {$\Delta$};
\tdplotsetmaincoords{\rotation}{180 - \zRotation}
\tdplotsetrotatedcoords{0}{90}{90}
\begin{scope}[tdplot_rotated_coords, xshift=-0.2cm, yshift=1.8cm]
% back edges
\path [draw, densely dotted] (0.4,-1.,1.8)--(1.333,-1.,-1.);
\path [draw, densely dotted] (1.333,-1.,-1.)--(-1.,2.5,-1.);
\path [draw, densely dotted] (-1.,2.5,-1.)--(0.4,-1.,1.8);
\path [draw, densely dotted] (1.333,-1.,-1.)--(-1.,-1.,-1.);
\path [draw, densely dotted] (-1.,-1.,-1.)--(-1.,2.5,-1.);
\path [draw, densely dotted] (-1.,-1.,-1.)--(0.4,-1.,1.8);
% back faces
\path [draw, fill opacity=\opacity, fill=fillColor] (-1.,-1.,-1.)--(0.,-1.,1.)--(0.,0.,1.)--(-1.,2.,-1.)--cycle;
\path [draw, fill opacity=\opacity, fill=fillColor] (-1.,-1.,-1.)--(-1.,2.,-1.)--(0.,1.,-1.)--(1.,-1.,-1.)--cycle;
\path [draw, fill opacity=\opacity, fill=fillColor] (0.,-1.,1.)--(-1.,-1.,-1.)--(1.,-1.,-1.)--(1.,-1.,0.)--cycle;
% back points
\point{-1.,-1.,-1.};
\point{-1.,0.,-1.};
\point{-1.,1.,-1.};
\point{0.,-1.,-1.};
\point{0.,-1.,0.}; % on face
\point{0.,0.,-1.}; % on face
\point{0.,0.,0.}; % inside
% front faces
\path [draw, fill opacity=\opacity, fill=fillColor] (0.,0.,1.)--(0.,1.,-1.)--(-1.,2.,-1.)--cycle;
\path [draw, fill opacity=\opacity, fill=fillColor] (0.,1.,-1.)--(1.,-1.,0.)--(1.,-1.,-1.)--cycle;
\path [draw, fill opacity=\opacity, fill=fillColor] (1.,-1.,0.)--(0.,1.,-1.)--(0.,0.,1.)--cycle;
\path [draw, fill opacity=\opacity, fill=fillColor] (1.,-1.,0.)--(0.,0.,1.)--(0.,-1.,1.)--cycle;
% front points
\point{1.,-1.,-1.};
\point{1.,-1.,0.};
\point{0.,1.,-1.};
\point{0.,-1.,1.};
\point{0.,0.,1.};
\point{-1.,2.,-1.};
\end{scope}
\end{scope}
\begin{scope}[yshift=-6.5cm]
\path [draw, -Stealth] (3.7, 2.7) -- node [above] {dual} (1.7, 2.7);
\node at (0, 0) {$\Delta^{\!*}$};
\tdplotsetmaincoords{\rotation}{-\zRotation}
\tdplotsetrotatedcoords{0}{90}{90}
\begin{scope}[tdplot_rotated_coords, xshift=0.2cm, yshift=3.4cm]
% back edges
\path [draw, fill opacity=\opacity, fill=fillColor] (0.,0.,1.)--(-2.,-2.,-1.)--(2.,0.,-1.) --cycle;
\path [draw, fill opacity=\opacity, fill=fillColor] (-3.,-2.,-1.)--(-2.,-2.,-1.)--(0.,0.,1.)--(-2.,-1.,0.) --cycle;
\path [draw, fill opacity=\opacity, fill=fillColor] (0.,1.,0.)--(0.,0.,1.)--(2.,0.,-1.) --cycle;
% back faces
\path [draw, densely dotted] (2.,0.,-1.)--(-3.,-2.,-1.);
\path [draw, densely dotted] (-3.,-2.,-1.)--(0.,1.,0.);
\path [draw, densely dotted] (0.,0.,1.)--(-3.,-2.,-1.);
% back points
\point{-1.,-1.,0.};
\point{1.,0.,0.};
\point{0.,0.,0.}; % inside
% front faces
\path [draw, fill opacity=\opacity, fill=fillColor] (-1.,0.,-1.)--(-3.,-2.,-1.)--(-2.,-1.,0.)--(0.,1.,0.) --cycle;
\path [draw, fill opacity=\opacity, fill=fillColor] (-1.,0.,-1.)--(0.,1.,0.)--(2.,0.,-1.) --cycle;
\path [draw, fill opacity=\opacity, fill=fillColor] (-1.,0.,-1.)--(2.,0.,-1.)--(-2.,-2.,-1.)--(-3.,-2.,-1.) --cycle;
\path [draw, fill opacity=\opacity, fill=fillColor] (-2.,-1.,0.)--(0.,0.,1.)--(0.,1.,0.) --cycle;
% front points
\point{-3.,-2.,-1.};
\point{-2.,-2.,-1.};
\point{-2.,-1.,-1.};
\point{-2.,-1.,0.};
\point{-1.,0.,-1.};
\point{-1.,0.,0.};
\point{0.,-1.,-1.};
\point{0.,0.,-1.};
\point{0.,0.,1.};
\point{0.,1.,0.};
\point{1.,0.,-1.};
\point{2.,0.,-1.};
\point{-1.,-1.,-1.}; % on face
\end{scope}
\end{scope}
% \begin{scope}[yshift=-6.5cm]
% \path [draw, -Stealth] (3.7, 2.7) --(1.7, 2.7);
% \node at (0, 0) {$\Delta^{\!*}$};
% \tdplotsetmaincoords{\rotation}{180 - \zRotation}
% \tdplotsetrotatedcoords{0}{90}{90}
% \begin{scope}[tdplot_rotated_coords, xshift=0.2cm, yshift=3.4cm]
% % back faces
% \path [draw, fill opacity=\opacity, fill=fillColor] (-1.,0.,-1.)--(-3.,-2.,-1.)--(-2.,-1.,0.)--(0.,1.,0.) --cycle;
% \path [draw, fill opacity=\opacity, fill=fillColor] (-1.,0.,-1.)--(0.,1.,0.)--(2.,0.,-1.) --cycle;
% \path [draw, fill opacity=\opacity, fill=fillColor] (-1.,0.,-1.)--(2.,0.,-1.)--(-2.,-2.,-1.)--(-3.,-2.,-1.) --cycle;
% \path [draw, fill opacity=\opacity, fill=fillColor] (-2.,-1.,0.)--(0.,0.,1.)--(0.,1.,0.) --cycle;
% % back points
% \point{-3.,-2.,-1.};
% \point{-2.,-2.,-1.};
% \point{-2.,-1.,-1.};
% \point{-2.,-1.,0.};
% \point{-1.,0.,-1.};
% \point{-1.,0.,0.};
% \point{0.,-1.,-1.};
% \point{0.,0.,-1.};
% \point{0.,0.,1.};
% \point{0.,1.,0.};
% \point{1.,0.,-1.};
% \point{2.,0.,-1.};
% \point{-1.,-1.,-1.}; % on face
% \point{0.,0.,0.}; % inside
% % front edges
% \path [draw, fill opacity=\opacity, fill=fillColor] (0.,0.,1.)--(-2.,-2.,-1.)--(2.,0.,-1.) --cycle;
% \path [draw, fill opacity=\opacity, fill=fillColor] (-3.,-2.,-1.)--(-2.,-2.,-1.)--(0.,0.,1.)--(-2.,-1.,0.) --cycle;
% \path [draw, fill opacity=\opacity, fill=fillColor] (0.,1.,0.)--(0.,0.,1.)--(2.,0.,-1.) --cycle;
% % front faces
% \path [draw, densely dotted] (2.,0.,-1.)--(-3.,-2.,-1.);
% \path [draw, densely dotted] (-3.,-2.,-1.)--(0.,1.,0.);
% \path [draw, densely dotted] (0.,0.,1.)--(-3.,-2.,-1.);
% % front points
% \point{-1.,-1.,0.};
% \point{1.,0.,0.};
% \end{scope}
% \end{scope}
\end{tikzpicture}
\end{document}
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