با جابه جایی دستورات و اضافه کردن دستور \fill=white
می توانید به خواسته خود برسید
\documentclass[10pt]{article}
\usepackage{pgf,tikz}
\usepackage{mathrsfs}
\usetikzlibrary{arrows}
\pagestyle{empty}
\begin{document}
\definecolor{qqqqff}{rgb}{0.,0.,1.}
\definecolor{xdxdff}{rgb}{0.49019607843137253,0.49019607843137253,1.}
\definecolor{uuuuuu}{rgb}{0.26666666666666666,0.26666666666666666,0.26666666666666666}
\begin{tikzpicture}[line cap=round,line join=round,>=triangle 45,x=1.0cm,y=1.0cm]
\clip(-11.221070518582748,-5.608880531320633) rectangle (13.716344537467586,7.011619957915192);
\draw (0.,4.)-- (-3.46,-2.);
\draw (3.47,-2.)-- (-3.46,-2.);
\draw (3.47,-2.)-- (0.,4.);
\draw (0.,-2.)-- (0.,0.);
\draw (0.,0.)-- (0.,4.);
\draw (-3.46,-2.)-- (0.,0.);
\draw (0.,0.)-- (1.735,1.);
\draw (3.47,-2.)-- (0.,0.);
\draw (0.,0.)-- (-1.73,1.);
\draw(0.,0.) circle (2.cm);
\draw[fill=white](0.,0.) circle (0.5cm)node[]{ $i$};
\draw[fill=white](0.,-2.) circle (0.5cm)node[]{ $i$};
\draw[fill=white](3.47,-2.) circle (0.5cm)node[]{ $i$};
\draw[fill=white](-3.46,-2.) circle (0.5cm)node[]{ $i$};
\draw[fill=white](0.,4.) circle (0.5cm)node[]{ $i$};
\draw[fill=white](-1.73,1.) circle (0.5cm)node[]{ $i$};
\draw[fill=white](1.735,1.) circle (0.5cm)node[]{ $i$};
\end{tikzpicture}
\end{document}
نتیجه به صورت زیر خواهد بود: