Wie kann ich berechnete Koordinaten-Punkte aus einer Schleife verbinden?

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\documentclass[margin=5pt]{standalone}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}[scale=2.5, >=latex,graph/.style={blue}]
\newcommand*\Beta{22.5}
% Hyperwürfel
\foreach \w in {0,1}
  \foreach \x in {0,1}
    \foreach \y in {0,1}
      \foreach \z in {0,1}
% X - Koordinate in Zeichenebene
        \pgfmathsetmacro{\X}{\w*cos(7*\Beta)+\x*cos(5*\Beta)+\y*cos(3*\Beta)+\z*cos(\Beta)}
% Y - Koordinate in Zeichenebene
        \pgfmathsetmacro{\Y}{\w*sin(7*\Beta)+\x*sin(5*\Beta)+\y*sin(3*\Beta)+\z*sin(\Beta)}
% Koordinate setzen
        \coordinate(\w\x\y\z) at ({\X},{\Y});
%Kanten zeichnen
\foreach \i in {0,1}\foreach \j in {0,1}{
  \draw[graph] (0\i\j0)--(0\i\j1)--(1\i\j1)--(1\i\j0)--cycle;
  \draw[graph] (\i00\j)--(\i10\j)--(\i11\j)--(\i01\j)--cycle;
}
%4D-Koordinatensystem:
\draw[->] (0,0) -- ({1.5*cos(7*\Beta)},{1.5*sin(7*\Beta)})  node[above]{$w$};
\draw[->] (0,0) -- ({1.5*cos(5*\Beta)},{1.5*sin(5*\Beta)}) node[above]{$x$};
\draw[->] (0,0) --({1.5*cos(3*\Beta)},{1.5*sin(3*\Beta)}) node[yshift=2mm]{$y$};
\draw[->] (0,0) -- ({1.5*cos(\Beta)},{1.5*sin(\Beta)}) node[xshift=2mm]{$z$};
%2D-Zeichenebene
\draw[->, gray]  (-1.5,0) --  (1.5,0) node[right]{$\bar{x}$};
\draw[->, gray]  (0,0) --  (0,1.5) node[above]{$\bar{y}$};
\end{tikzpicture}
\end{document}
 
 
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