5

Is there a way to draw only the vertices of the triangles?

\begin{tikzpicture}[x=1mm, y=1mm]

    \coordinate (A) at (0:12);
    \coordinate (B) at (120:12);
    \coordinate (C) at (240:12);

    \foreach \i in {0, 1, ..., 9}{

        \draw[line width=0.1mm] (A) -- (B) -- (C) -- cycle;

        \path
             (A) coordinate (X)
          -- (B) coordinate[pos=0.2] (A)
          -- (C) coordinate[pos=0.2] (B)
          -- (X) coordinate[pos=0.2] (C);
    }

\end{tikzpicture}

enter image description here

The edges of the first triangle should be visible.

6

insert path is pretty convenient for such things

\begin{tikzpicture}[scale=.5,c/.style={insert path={node[inner sep=2pt,fill,circle]{}}}]
  \coordinate (A) at (0:12);
  \coordinate (B) at (120:12);
  \coordinate (C) at (240:12);
  \draw[line width=0.1mm] (A) -- (B) -- (C) -- cycle;
  \foreach \i in {0, 1, ..., 9}{
    \path  (A) [c]coordinate (X)
        -- (B) [c]coordinate[pos=0.2] (A)
        -- (C) [c]coordinate[pos=0.2] (B)
        -- (X)    coordinate[pos=0.2] (C);
  }
\end{tikzpicture}

enter image description here

  • 1
    The [c] for (X) is not needed, because the circle is already drawn at the beginning for (A). Nice idea +1. – Heiko Oberdiek Aug 20 '15 at 17:56
  • @HeikoOberdiek Just copy/pasting too fast. I wasn't thinking apparently. Thanks – percusse Aug 20 '15 at 18:45
5

The solution of percusse without insert path and with a little smaller circles:

\documentclass{article}
\usepackage{tikz}

\begin{document}
\begin{tikzpicture}[scale=.5]
  \coordinate (A) at (0:12);
  \coordinate (B) at (120:12);
  \coordinate (C) at (240:12);
  \draw[line width=0.1mm] (A) -- (B) -- (C) -- cycle;
  \path[               
    every node/.style={circle, fill, inner sep=1.5pt},
  ]
    \foreach \i in {0, 1, ..., 9}{
         (A) node (X) {}
      -- (B) node{} coordinate[pos=0.2] (A)
      -- (C) node{} coordinate[pos=0.2] (B)
      -- (X.center) coordinate[pos=0.2] (C)
    }
  ;
\end{tikzpicture}
\end{document}

Result

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