\documentclass[a4paper,11pt]{article}

\usepackage{ngerman}
\usepackage{amsmath,amsfonts,amssymb,amsthm}

\usepackage{tikz}
\usetikzlibrary{arrows,chains,matrix,positioning,scopes}
\usetikzlibrary{arrows.meta}
\usetikzlibrary{math}

\def\O{\mathcal{O}}
\def\sort{\mathrm{sort}}
\def\scan{\mathrm{scan}}
\def\dist{\mathrm{dist}}
\def\Z{\mathbb{Z}}
\def\Q{\mathbb{Q}}
\def\R{\mathbb{R}}
\def\E{\mathbb{E}}


\begin{document}


\textbf{Aufgabe 3}
\begin{center}
	\begin{tikzpicture}[vertex_style/.style={draw,circle,thick,inner sep=2.5pt},edge_style/.style={thick}]
	\begin{scope}[rotate=270]
	\foreach \x/\y in {0/1,72/2,144/3,216/4,288/5}{
		\node[vertex_style] (\y) at (canvas polar cs: radius=7.5mm,angle=\x){};
	}
	\foreach \x/\y in {0/6,72/7,144/8,216/9,288/10}{
		\node[vertex_style] (\y) at (canvas polar cs: radius=15mm,angle=\x){};
	}
	\end{scope}
	
	\foreach \x/\y in {1/6,2/7,3/8,4/9,5/10}{
		\draw[edge_style] (\x) -- (\y);
	}
	
	\foreach \x/\y in {1/3,2/4,3/5,4/1,5/2}{
		\draw[edge_style] (\x) -- (\y);
	}
	
	\foreach \x/\y in {6/7,7/8,8/9,9/10,10/6}{
		\draw[edge_style] (\x) -- (\y);
	}
	
%	\fill[red!60!black] ( 1) circle (3pt);
	
	\end{tikzpicture}
\end{center}


\end{document}