Problem with drawing 16-sided shape in TikZ

Like this?

\documentclass[]{article}
\usepackage{tikz}
\tikzset{
  pics/diamond/.style args={name=#1}{
    code={
      \begin{scope}[local bounding box=#1,scale=0.5]
        \draw (0,0)--++(0:1)--++(-45:1.2)--++(45:1.2)--++(0:1)--++(90:1)--++(45:1.2)--++(135:1.2)--++(90:1)--++(180:1)--++(135:1.2)--++(225:1.2)--++(180:1)--++(-90:1)--++(-135:1.2)--++(-45:1.2)--cycle;
      \end{scope}
    }
  }
}

\begin{document}
\begin{tikzpicture}
\pic at (0,0) {diamond={name=a}};
\node at (a.center){\thepage};
\end{tikzpicture}

\end{document}

\documentclass[tikz, margin=3mm]{standalone}
\setcounter{page}{111}
\newcommand\PAGE%
{
\begin{tikzpicture}[
  box/.style args = {##1/##2}{draw, minimum size=\dimexpr9mm-##1\pgflinewidth, 
                            rotate=##2, fill=white},
                    ]
\node [box=0/0] {};
\node [box=0/45] {};
\node [box=1/0, draw=none] {\thepage};
\end{tikzpicture}
}

\begin{document}
\PAGE
\end{document}

These shapes are known as stars. You can play with the star point ratio.

\documentclass[tikz,border=3.14mm]{standalone}
\usetikzlibrary{shapes.geometric}
\begin{document}
\begin{tikzpicture}
 \node[draw,star,star points=8]{hello}; 
 \node[draw,star,star points=8,star point ratio=1.25] at (3,0) {hello};
 \node[draw,star,star points=8,star point ratio=0.8] at (6,0) {hello};
\end{tikzpicture}
\end{document}