Q:

How to draw an octagon with a star internally?

\documentclass {article}
\usepackage{tikz}
\usetikzlibrary{shapes.geometric}
\begin{document}
\foreach \n in {8}
  \tikz\foreach \i in {1,...,\n}
    \fill (\i*360/\n:1) coordinate (n\i) circle(2 pt)
     \ifnum \i>0 foreach \j in {\i+1,\i+4}{(n\i) edge (n\j)} \fi;

\end{document}

which leads to:

I want to make an octagon with this type of edges, but I don't know why the edges bewteen \i and \i+1 are not showing up. Any suggestions would be great!

A:

Welcome! Since you are loading shapes.geometric, you could just do
\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{shapes.geometric}
\begin{document}
\begin{tikzpicture}[dot/.style={circle,fill,inner sep=0pt,minimum size=4pt}]
 \draw node[regular polygon,regular polygon sides=8,draw,minimum size=2cm]
 (p8){}
  foreach \X[count=\Y] in {5,...,8} {(p8.corner \X) node[dot](n-\X){}
    -- (p8.corner \Y) node[dot](n-\Y){} };
\end{tikzpicture}
\end{document}

However, there are IMHO better tools available: the graphs library. While it is true that there are not as many examples for those on this site available as for the above (which appeared several times in slight variations), I think this one will be much more powerful if you are really into graph drawing. 
\documentclass[tikz,border=3mm]{standalone}
\usetikzlibrary{graphs,graphs.standard}
\begin{document}
\begin{tikzpicture}
\begin{scope}[nodes={circle,fill,inner sep=0pt,minimum size=4pt}]
 \graph[empty nodes] { 
  {subgraph C_n [n=8,radius=1cm, counterclockwise] -- 
    0[coordinate]}; 
    };
\end{scope}
\end{tikzpicture}
\end{document}

