A regular pentagon has the following dimensions:
AB=BC=CD=DE=AE=BG=EG=1
AC=AD=BD=BE=CE=Φ
BF=EF=Φ/2 = cos 36 = sin 54 = \(\frac{1+\sqrt{5}}{4}\)
CG=DG= Φ-1 = 1/Φ = \(\frac{\sqrt5-1}{2}\)
AF=FG= cos 54 = sin 36 = \(\sqrt{\frac{5-\sqrt5}{8}}\)
AG= 2cos 54 = 2sin 36= \(\sqrt{\frac{5-\sqrt5}{2}}\)
CH=DH=BK=CK=1/2
Height AH=EK=\(\frac12\cos 18 = \frac12\sin 72 = \frac12\sqrt{5+2\sqrt5}\)
Circumradius AJ=\(\sqrt{\frac{5+\sqrt5}{10}}\) = BJ=CJ=DJ=EJ
Inradius JK=HJ= \(\sqrt{\frac{5+2\sqrt5}{20}} \) = \(\frac{AH}{\sqrt5}\)
FH= cos 18 =sin 72 = \(\sqrt{\frac{5+\sqrt5}{8}}\)
FJ=JK/Φ
GJ=AJ/Φ
GH=AF/Φ=\(\frac12\sqrt{5-2\sqrt5}\)
ABGE is a equilateral rhombus, with angles {108°, 54°, 108°, 54°} and diagonals of length Φ and \(\sqrt{\frac{5-\sqrt5}{2}}\).
The small pentagon in the center has sides \(1/\Phi^2 = \frac{3-\sqrt5}{2}\) times that of the larger.