Polygon with numbered vertices

Question

About this, I'd like to numerate vertices of pentagon with a cyclic tikz function (e.g. \pgfmathtruncatemacro). How is it possible? Thank you!

The code

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage{tikz}

\usetikzlibrary{shapes.geometric}

\usepackage{pst-node,pst-plot}

\title{Polygon with numbered vertices}
\author{PUCK}
\date{\today}


\begin{document}

\maketitle

\section{Introduction}

\begin{center}
\def\R{2} \def\N{5}
\begin{tikzpicture}[baseline ={(0,0)}]
\foreach \i in {1,...,\N} { \coordinate (P-\i) at (\i*360/\N+90/\N:\R); }
\pgfmathtruncatemacro\n{\N-1} 
\foreach \i in {1,...,\n}
   {
      \pgfmathtruncatemacro\j{\i+1}       
      \draw (P-\i) -- (P-\j) ;
   } 
\draw (P-\N) -- (P-1) ;
\draw (0,0) node {\Huge{$P_n$}} ;
\draw (0,0) circle (2cm) ;
\draw[->] (-2.5,0) -- (3.5,0) coordinate (x axis);
\draw (2.75,0) circle (0pt) node[anchor=north] {asse $x$};
\draw[->] (0,-2.5) -- (0,2.5) coordinate (y axis);
\draw (0,2.4) circle (0pt) node[anchor=north west] {asse $y$};
\end{tikzpicture}
\end{center}

\end{document}

Answer 1

Simplest way I can think off is to declare another coordianate for the (P-\i') at which to place the label, where we tweak the label for point 2:

\foreach \i in {0,...,\N} { 
    \coordinate (P-\i) at (\i*360/\N+90/\N:\R); 
    \ifnum\i=1
        \def\LabeAngle{105}
    \fi
    \coordinate (P-\i') at (\i*360/\N+\LabeAngle/\N:1.1*\R); 
}

and then place the label via

\coordinate (P-\i') at (\i*360/\N+\LabeAngle/\N:1.1*\R)

A better solution is to use the regular polygon from the shapes.geometric:

\node [
    regular polygon, 
    regular polygon sides=5, 
    minimum size=2*\R cm, 
    draw=black, fill=gray!25, thick
] 
at (0,0) {};

This is the code below, with the commented portions representing the first version.

References:

• A similar question: A pentagon with labeled edges

Code:

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage{tikz}

\usetikzlibrary{shapes.geometric}

\usepackage{pst-node,pst-plot}

\title{Polygon with numbered vertices}
\author{PUCK}
\date{\today}
\pagecolor{white}

\begin{document}

\maketitle

\section{Introduction}

\begin{center}
\def\R{2} \def\N{5}
\def\LabeAngle{90}
\begin{tikzpicture}[baseline ={(0,0)}]
\foreach \i in {0,...,\N} { 
    \coordinate (P-\i) at (\i*360/\N+90/\N:\R); 
    \ifnum\i=1
        \def\LabeAngle{105}
    \fi
    \coordinate (P-\i') at (\i*360/\N+\LabeAngle/\N:1.1*\R); 
}
\pgfmathtruncatemacro\n{\N-1} 
\node [regular polygon, regular polygon sides=5, minimum size=2*\R cm, draw=black, fill=gray!25, thick] at (0,0) {};
\foreach \i in {0,...,\n}
   {
      %\pgfmathtruncatemacro\j{\i+1}       
      %\draw (P-\i) -- (P-\j) ;
      \pgfmathtruncatemacro\NodeLabel{1+\i}
      \node at  (P-\i') {$\NodeLabel$};
   } 
%\draw (P-\N) -- (P-1) ;
\draw (0,0) node {\Huge{$P_n$}} ;
\draw (0,0) circle (2cm) ;
\draw[->] (-2.5,0) -- (3.5,0) coordinate (x axis);
\draw (2.75,0) circle (0pt) node[anchor=north] {asse $x$};
\draw[->] (0,-2.5) -- (0,2.5) coordinate (y axis);
\draw (0,2.4) circle (0pt) node[anchor=north west] {asse $y$};
\end{tikzpicture}
\end{center}
\end{document}

Answer 2

For comparison, here is a way of doing that in Metapost.

\documentclass[border=5mm]{standalone}
\usepackage{luamplib}
\begin{document}
\mplibtextextlabel{enable}
\begin{mplibcode}
input colorbrewer-rgb
numeric r; r = 42;
path xx, yy, C;
xx = (left--right) scaled 3/2 r;
yy = xx rotated 90;
C = fullcircle scaled 2r;
ahangle := 25;
beginfig(1);
for n=3 upto 8:
    path poly; poly = for i=0 upto n-1: r * up rotated (360/n*(i-1)) -- endfor cycle;
    picture P; P = image(
        fill poly withcolor PastelOne[9][n];
        drawarrow xx withcolor 3/4;
        drawarrow yy withcolor 3/4;
        draw C withcolor 3/4;
        draw poly;
        label("$P_{" & decimal n & "}$", origin);
        % this scaling trick works because the poly is centered at (0,0)
        for i=1 upto n:
            label("$" & decimal i & "$", point i of poly scaled (1+6/r));
        endfor
    );
    draw P shifted ((n mod 3, -floor(n/3)) scaled 3.5r);
endfor
endfig;
\end{mplibcode}
\end{document}

You need to compile this with lualatex so that the luamplib wrapper works.