Draw star polymer in tikz

Here is a starting point for you, using the decorations.markings library of tikz as suggested by percusse. You just need to adjust the path in the way you want, to draw the 'star' correctly and the decoration of the path is done by tikz. By the way, is there any good reason, why you've started to define your coordinates in 3 dimensions? At least for getting the picture as shown in your question, this is not necessary.

\documentclass[tikz, border=3mm]{standalone}
\usetikzlibrary{decorations.markings}
%
\begin{document}
%
\begin{tikzpicture}[
    decoration={
        markings,% switch on markings
        mark=% actually add a mark
        between positions 0 and 1 step 4mm % tells tikz to decorate path from beginning to end (0,1) and every 4 mm (diameter of the balls) defined two lines later
        with
            {\shade[ball color=red!80] (0,0) circle (.2cm);}% this is the definition of the actual marking.
        }
    ]
%
\path[postaction={decorate}] (0,0) .. controls (.5,1) and (1,1) .. (1.5,2);% postaction={decorate} tells tikz to decorate the path after it has been created. Note that \path itself doesn't draw anything but just creates the path to decorate.
\path[postaction={decorate}] (0,0) .. controls (-2,-1) and (-1,-2) .. (-1.5,-2);
\path[postaction={decorate}] (0,0) .. controls (1,-1) and (-1,-2) .. (1.5,-2);
\path[postaction={decorate}] (0,0) .. controls (-1,1) and (0,1.5) .. (-1.5,2);
\shade[ball color=blue!60] (0,0) circle (.2cm);% draw a blue ball over the red one in the center
%
\end{tikzpicture}%
%
\end{document}