from numpy import exp, pi, arange
import matplotlib.pyplot as plt

# Vertices of a hexagon
hexa = exp(2j*pi*arange(6)/6)

# Vertices of a decagon, shifted and rotated
# to have a side perpendicular to the hexagon
deca = exp(2j*pi*(0.5+arange(10))/10)
deca += hexa[1] - deca[5]

# Shift and rotate a pentagon to share one vertex 
# with the hexagon and one vertex with the decagon
omega = exp(2j*pi/5)
c = (hexa[2]*omega - deca[4])/(omega - 1)
penta = c + (hexa[2] - c)*exp(2j*pi*arange(5)/5) 

def connect(p, q, c):
	plt.plot([p.real, q.real], [p.imag, q.imag], '-', color=c)

plt.gca().set_aspect("equal")

for n in range(-1, 5):
	connect(hexa[n], hexa[n+1], 'blue')
for n in range(-1, 9):
	connect(deca[n], deca[n+1], 'green')
for n in range(-1, 4):
	connect(penta[n], penta[n+1], 'red')

plt.show()