Tikz: Fill the intersection between two polygons

Question

I'm trying to fill the intersection of the two polygons that I have made using tikz. But it seems like I have some mistake in my \clip and \fill commands that I can't get what I want. This is what I want actually:

Here's the TeX script that I wrote for that purpose:

\documentclass[english]{scrreprt}
\usepackage{tikz}
\usetikzlibrary{shapes,calc,intersections}

\begin{document}
\begin{figure}
   \centering
   \begin{tikzpicture}[scale=2.5]

   \node    [draw, regular polygon,regular polygon sides=5,rotate=85,scale=8., name = A] at (0.3,0) {}; 
   \node    [draw, regular polygon,regular polygon sides=7,rotate=80,scale=10, name = B] at (1.4,0) {};

   \begin{scope}
       \clip (0.3,0)    [regular polygon,regular polygon sides=5,rotate=85,scale=8.];
       \fill [orange]   (1.4,0) [regular polygon,regular polygon sides=7,rotate=80,scale=10];
   \end{scope}

   \end{tikzpicture}
\end{figure}
\end{document}

As you can see I need the coordinates of the centroids of the two polygons, otherwise I would have used simply the \draw command to draw them.

Thanks a ton!

Answer 1

I can explain why your code for filling the intersection doesn't work. You're using a node as clipping path and a node is not a path, as soon as you could declare a real path for clipping, the intersection will be filled.

Next command defines a closed path around regular polygon corners

\clip (A.corner 1) foreach \i in {2,3,4,5} {--(A.corner \i)} --cycle;

which can be used to clip a reproduction of second polygon

\node[fill=orange, regular polygon,regular polygon sides=7,rotate=80,scale=10] at (1.4,0) {};

Note that also outer sep=0pt has been added in first regular polygon because otherwise scale option moves corner anchors. I don't know why (probably related with this Note 1).

\documentclass[border=2mm,tikz]{standalone}
\usepackage{tikz}
\usetikzlibrary{shapes,calc,intersections}

\begin{document}
   \begin{tikzpicture}[scale=2.5]

   \node[draw, shape=regular polygon,regular polygon sides=5,rotate=85,scale=8., name = A, outer sep=0pt] at (0.3,0) {}; 
   \node[draw, regular polygon,regular polygon sides=7,rotate=80,scale=10, name = B] at (1.4,0) {};

   \begin{scope}
       \clip (A.corner 1) foreach \i in {2,3,4,5} {--(A.corner \i)} --cycle;
       \node[fill=orange, regular polygon,regular polygon sides=7,rotate=80,scale=10] at (1.4,0) {};
   \end{scope}

   \end{tikzpicture}
   \end{document}