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I am trying to draw the following three figures that all involve a center point with arrows pointing to the outer vertexes. The first and third are on a grid. The second involves the center of a cube and the arrows point to the eight vertexes.

I have tried using tikzcd, but am not sure how to draw the grid or access the center of the cube.

figures

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For the 3d-like drawing I recommend tikz-3dplot.

\documentclass[tikz,border=3.14mm]{standalone}
\usepackage{tikz-3dplot}
\begin{document}
\begin{tikzpicture}[line join=miter] 
 \draw[thick] (-1.9,-1.9) grid (1.9,1.9);
 \draw[thick,latex-latex] (-1,-1) -- (1,1);
 \draw[thick,latex-latex] (-1,1) -- (1,-1);
 \fill (0,0) circle (2pt);
 %
 \tdplotsetmaincoords{70}{-30}
 \begin{scope}[xshift=5cm,tdplot_main_coords]
  \draw[dashed] (-1,1,-1) -- (1,1,-1) -- (1,-1,-1)  (1,1,-1) -- (1,1,1);
  \draw[thick] (1,1,1) -- (1,-1,1) -- (-1,-1,1) -- (-1,1,1) -- cycle
  (1,-1,1) -- (1,-1,-1) -- (-1,-1,-1) -- (-1,1,-1) -- (-1,1,1)
  (-1,-1,-1) -- (-1,-1,1);
  \foreach \X in {-1,1}
  {\foreach \Y in {-1,1}
   {\foreach \Z in {-1,1}
    {\draw[-latex] (0,0,0) -- (\X,\Y,\Z);}}}
  \fill (0,0,0) circle (2pt);   
 \end{scope}
 %
 \begin{scope}[xshift=10cm]
  \draw[thick] (-1.9,-1.9) grid (1.9,1.9);
  \draw[thick,latex-latex] (-1,0) -- (1,0);
  \draw[thick,latex-latex] (0,1) -- (0,-1);
  \fill (0,0) circle (2pt); 
 \end{scope}
\end{tikzpicture}
\end{document}

enter image description here

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