How to draw the figure with four pentagons?

Question

I want to make the next figure formed by 4 pentagons.

I can only do with two and still have a space between them. I can't even do the reflection of the two pentagons to get the desired figure.

\documentclass[a4paper]{article}

\usepackage[brazil]{babel}

\usepackage{graphicx}

\usepackage{tikz}

\begin{document}

 \begin{center}

\begin{figure}[!htb]

  \begin{tikzpicture}

        \draw[ultra thick,rotate=18] (0:2) -- (72:2) -- (144:2) -- (216:2) -- (288:2) -- cycle;

  \end{tikzpicture}

 \end{figure}

\begin{figure}[!htb]

   \begin{tikzpicture}
        \draw[ultra thick,rotate around={198:(-0.80,0.58)}] (0:2) -- (72:2) -- (144:2) -- (216:2) -- (288:2) -- cycle;

  \end{tikzpicture}

  \end{figure}

\end{center}

\end{document}

Answer 1

You can draw more than one shape in the same tikzpicture:

\documentclass[a4paper]{article}

\usepackage[brazil]{babel}

\usepackage{graphicx}

\usepackage{tikz}

\begin{document}

 \begin{center}

\begin{figure}[!htb]

  \begin{tikzpicture}

        \draw[ultra thick,rotate=18] (0:2) -- (72:2) -- (144:2) -- (216:2) -- (288:2) -- cycle;
        \begin{scope}[yshift=-3.22cm]
        \draw[ultra thick,rotate=198] (0:2) -- (72:2) -- (144:2) -- (216:2) -- (288:2) -- cycle;
                \end{scope}
                \begin{scope}[xshift=3.8cm]
                        \draw[ultra thick,rotate=18] (0:2) -- (72:2) -- (144:2) -- (216:2) -- (288:2) -- cycle;
                        \begin{scope}[yshift=-3.22cm]
                        \draw[ultra thick,rotate=198] (0:2) -- (72:2) -- (144:2) -- (216:2) -- (288:2) -- cycle;
                                \end{scope}
                \end{scope}
  \end{tikzpicture}

  \end{figure}

\end{center}

\end{document}

---

To make things easier, you can use predefined pentagons:

\documentclass[a4paper]{article}

\usepackage{tikz}
\usetikzlibrary{shapes.geometric}

\begin{document}

\begin{figure}[!htb]
\begin{tikzpicture}[every node/.append style={regular polygon, regular polygon sides=5, minimum size=4cm, draw,ultra thick}]
    \node at (0,0) {};
    \node at (3.8,0) {};    
    \node[rotate=180] at (0,-3.22) {};  
    \node[rotate=180] at (3.8,-3.22) {};        
\end{tikzpicture} 
\end{figure}

\end{document} 

Off-topic: please note that placing a floating figure environment inside a non-floating center environment does not make much sense..

Answer 2

Similar answer to @samcarter, but using named nodes -- avoids having to calculate the distances. My motto: Let TikZ do the work!

\documentclass{article}

\usepackage{tikz}

\usetikzlibrary{shapes.geometric}
%% The size can easily altered by changing the minimum size
\tikzset{pgon/.style={regular polygon,regular polygon sides=5,minimum size=1in,draw,ultra thick,outer sep=0pt}}

\documentclass{article}

\usepackage{tikz}

\usetikzlibrary{shapes.geometric}

\tikzset{pgon/.style={regular polygon,regular polygon sides=5,minimum size=1.5in,draw,ultra thick,outer sep=0pt}}

\begin{document}

\tikz{%
    \node[pgon] (S) at (0,0) {S};
    \node[pgon,anchor=corner 2] (A) at (S.corner 5) {A};
    \node[pgon,rotate=180,anchor=corner 4] (B) at (S.corner 3) {B};
    \node[pgon,rotate=180,anchor=corner 4] (C) at (A.corner 3) {C};
    \draw[fill=purple!50,line join=bevel,ultra thick] (S.corner 5) --
            (A.corner 3) -- 
            (C.corner 5) -- 
            (S.corner 4) -- cycle;
}

\end{document}

Update

I have modified the code slightly so that there won't be a problem with mitre issues at the top and bottom of the colored shape. Updated the output as well.

Answer 3

This looks like a code golfing challenge ;)

\documentclass[tikz,border=7pt]{standalone}
\usetikzlibrary{shapes.geometric}
\begin{document}
  \tikz
    \path[fill=violet](1,1.17557)foreach~in{1,-1}{[scale=~]foreach~in{1,-1}{[yscale=~]
      --(1,1.17557)node[regular polygon,regular polygon sides=5,
      inner sep=17.11435,draw,fill=white,transform shape,yshift=-9.24486]{}}};
\end{document}

Calculations

• 1cm = 28.452755906694 pt
• x = 1 cm
• y = (cos(pi/5)+cos(2*pi/5))/sin(2*pi/5) = 1.1755705045849463 cm
• inner sep = cos(pi/5)/sqrt(2)/sin(2*pi/5)*28.452755906694 = 17.114359850473026 pt
• yshift = -cos(2*pi/5)/sin(2*pi/5)*28.452755906694 = -9.244860806192047 pt