antipedal vertices wrt f1: [(1, sqrt(13/20 - sqrt(3)/5)), (-sqrt(3)/2, -sqrt(5)/5), (-1, -sqrt(sqrt(3)/5 + 13/20)), (-1, sqrt(sqrt(3)/5 + 13/20)), (-sqrt(3)/2, sqrt(5)/5), (1, -sqrt(13/20 - sqrt(3)/5))]
distinct finite vertices: 6
signed area antipedal f1 = 0   f2 = 0
signed area pedal f1 = 50*sqrt(5)/81   f2 = 50*sqrt(5)/81
