All numbers on this page are in phinary. i.e. base \phi=\frac{\sqrt{5}+1}{2}.
10 = \phi,+ 0.1 = 1/\phi.
Since \phi^2=\phi+1, +1=0.11=1/\phi+1/\phi^2=\frac{\phi+1}{\phi^2}=1.
Measuring the (perpendicular) distance from each side in turn, anti-clockwise starting with the base, the coordinates for the top of the pentagon are (1,0.1,0,0,0.1). The coordinates of interior points add to 1.2=\sqrt{5}=0.221=10.1=2.001=1.022=0.31=0.132 etc.
Since \phi=\frac{\sqrt{5}+1}{2}, \sqrt{5}=2\phi-1:
\displaystyle 1.2=1+\frac{2}{\phi}=\frac{\phi+2}{\phi}=\frac{2(\phi+1)-\phi}{\phi}=\frac{2\phi^2-\phi}{\phi}=2\phi-1.
i.e. \sqrt{5}=1.2=20-1.

The similarity of 1=0.11 to the Fibonacci sequence rule F_n=F_{n-1}+F_{n-2} isn’t a coincidence – the ratio of successive Fibonacci terms goes to \phi as n increases.