Communications of the
Korean Mathematical Society CKMS

Based on a $n$-regular polygon $P_n$, we show that $r_n =1/(2 \displaystyle{\sum^{[(n-4)/4]+1}_{j=0}}\cos 2j\pi/n)$ is the ratio of contractions $f_i(1 \leq i \leq n)$ at each vertex of $P_n$ yielding a symmetric gasket $G_n$ associated with the just-touching I.F.S. $\Cal G_n = \{f_i \vert 1 \leq i \leq n\}$. Moreover we see that for any odd $n$, the ratio $r_n$ is still valid for just-touching I.F.S. $\Cal H_n = \{f_i \circ R \vert 1 \leq i \leq n \}$ yielding another symmetric gasket $H_n$ where $R$ is the $\pi / n$-rotation with respect to the center of $P_n$.

Keywords: Fractal gasket, Scaling factor, Iterated function system

MSC numbers: Primary 28A80, Secondary 58F08