Details for Pentadentrite IFS
Description
The coordinates of the five points can be determined using trigonometry. Recall that the scaling factor is \(r = \sqrt{\frac{{6 - \sqrt 5 }}{31}} = 0.34845\) and $A$ = 11.81858573°.
calculations
(pdf)
\(P1 = \left[ {\begin{array}{l}
{r\cos (A)} \\
{r\sin (A)} \\
\end{array}} \right] = \left[ {\begin{array}{r}
{0.34106} \\
{0.07137} \\
\end{array}} \right]\)
\(P2 = P1 + \left[ {\begin{array}{l}
{r\cos (72^ \circ + A)} \\
{r\sin (72^ \circ + A)} \\
\end{array}} \right] = \left[ {\begin{array}{r}
{0.37858} \\
{0.41779} \\
\end{array}} \right]\)
\(P3 = P2 + \left[ {\begin{array}{l}
{r\cos (A)} \\
{r\sin (A)} \\
\end{array}} \right] = \left[ {\begin{array}{r}
{0.71965} \\
{0.48916} \\
\end{array}} \right]\)
\(P4 = P3 + \left[ {\begin{array}{l}
{ - r\cos (36^ \circ + A)} \\
{ - r\sin (36^ \circ + A)} \\
\end{array}} \right] = \left[ {\begin{array}{r}
{0.48567} \\
{0.23095} \\
\end{array}} \right]\)
\(P5 = P4 + \left[ {\begin{array}{r} {r\cos (72^ \circ - A)} \\ { - r\sin (72^ \circ - A)} \\ \end{array}} \right] = \left[ {\begin{array}{r} {0.65894} \\ { - 0.07137} \\ \end{array}} \right]\)
