The picture is the following:

enter image description here

What would be the latex equivalent code ?

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    Welcome to TeX.SX! The short answer is that, yes, it is possible to do this but I have to warn you that questions of the form "Please draw this for me", which show no effort on the part of OP, often don't get answered. You will get more help if you post some code showing what you have tried and give a minimal working example. A quick search on TeX.SX for drawing functions (with tikz or pstricks) will give you an idea of where to start from. – Andrew Nov 9 '17 at 14:42
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    There is a similar example here: tex.stackexchange.com/questions/141624/… – Sebastiano Nov 9 '17 at 20:38
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    @cehptr :-). We are here to help each other because we do not have to be selfish but always leave some good memories. – Sebastiano Nov 10 '17 at 10:12

Thanks to Sebastian, an answer would be:

   \begin{polaraxis}[grid=none, axis lines=none]
     \addplot[mark=none,domain=0:360,samples=300] {0.1 +  abs(cos(4*x/2))};
   \node at (3.45, 3.45) {$\mathcal{O}$};
   \node at (3.45, 5.45) {\small{\textbf{(0,2)}}};
   \node at (3.45, 4.8) {\small{\textbf{(0,9)}}};
   \node at (5.25, 3.65) {\small{(8, i)}};
   \node at (5.25, 3) {\small{(8, 10i)}};
   \node at (1.65, 3.65) {\small{(2i+7, i)}};
   \node at (1.65, 3) {\small{(2i+7, 10i)}};
   \node at (3.45, 2.1) {\small{(9i+7,i)}};
   \node at (3.45, 1.45) {\small{(9i+7,10i)}};
  • Please also put preamble and figure; can you do it? – Sebastiano Nov 10 '17 at 10:13

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