Adding points inside a regular hexagon

I am trying to create this image with latex, and I specifically add the red points in the interior of the regular hexagon as well as make the outer edges of the regular hexagon blue.

I am able to create the following regular hexagon but I do not know how to color the outer edges blue or add the points in the interior (these points should specifically be on the intersection points of the diagonals):

\begin{tikzpicture}[
dot/.style={circle,fill, inner sep=1.5pt, outer sep=0pt},
every label/.style={inner sep=0pt}]
\newdimen\R
\R=1.3cm
\draw[red]
(300:\R) \foreach \x in {360,60} {  -- (\x:\R) };
\foreach \i [count=\j] in {1,2,3,4,5,6}
{
\node (n\j) [dot] at (60*\j:\R) {};
}
\foreach \i in {1,...,6}
{
\ifnum\i=1
\foreach \j in {2,...,6}
\draw (n\i) -- (n\j);
\else
\foreach \j in {\i,...,6}
\draw (n\i) -- (n\j);
\fi
}
\end{tikzpicture}


So here it is. Using my previous answers to two of your questions, here's a way to find intersections between lines defined between nodes:

\node at (intersection of n2--n6 and n1--n3) (A) {}; is pretty straightforward to understand. You named your nodes n1 to n6, you then put a node named A (not mandatory to name it, but allow you to use it afterwards) at the intersection of the line through nodes n2 and n6 and the line through n1 and n3.

I let you make the remaining ones. Note that you can also do them with a foreach loop, if you want to shorten your code.

\documentclass[tikz,border=3.14mm]{standalone}
\usetikzlibrary{backgrounds}

\begin{document}

\begin{tikzpicture}[
dot/.style={black,circle,fill, inner sep=1.5pt, outer sep=0pt,text=white},
innode/.style={inner sep=1.5pt,outer sep=0pt,circle,fill=red},
every label/.style={inner sep=0pt}]
\newdimen\R
\R=1.3cm

\draw[cyan,line width=1pt] (0:\R) \foreach \x [count=\i] in {60,120,...,360} {  -- (\x:\R) node[dot] (n\i) {} };

\begin{scope}[on background layer]
\foreach \i in {1,...,6}
{
\ifnum\i=1      % Part with \if is useless here, but anyway
\foreach \j in {2,...,6}
\draw (n\i.center) -- (n\j.center);
\else
\foreach \j in {\i,...,6}
\draw (n\i.center) -- (n\j.center);
\fi
}
\end{scope}

\node[innode] at (intersection of  n2--n6 and n1--n3) (A) {};
\node[innode] at (intersection of  n2--n5 and n1--n3) (B) {};
\end{tikzpicture}

\end{document}


You might also like a Metapost version, perhaps?

\documentclass[border=5mm]{standalone}
\usepackage{luamplib}
\begin{document}
\begin{mplibcode}
beginfig(1);
path h;
h = for t=0 upto 5: 72 dir 60t -- endfor cycle;

z0 = whatever[point 0 of h, point 2 of h] = whatever[point 1 of h, point 5 of h];
z1 = whatever[point 0 of h, point 2 of h] = whatever[point 1 of h, point 3 of h];
z2 = whatever[point 5 of h, point 2 of h] = whatever[point 1 of h, point 3 of h];
z3 = whatever[point 5 of h, point 3 of h] = whatever[point 2 of h, point 4 of h];
z4 = whatever[point 5 of h, point 3 of h] = whatever[point 0 of h, point 4 of h];
z5 = whatever[point 5 of h, point 2 of h] = whatever[point 0 of h, point 4 of h];

draw h withpen pencircle scaled 3 withcolor 3/4[blue, white];

for i=0 upto 5:
for j=i+1 upto 5:
draw point i of h -- point j of h;
endfor
endfor

for i=0 upto 5:
drawdot point i of h withpen pencircle scaled 5;
drawdot z[i]         withpen pencircle scaled 5 withcolor 2/3 red;
endfor
endfig;
\end{mplibcode}
\end{document}


This is wrapped up in luamplib, so compile with lualatex.