N = 6, a^2 = 1, b^2 = 1/4, lambda = 1/9 (a''^2 = 8/9, b''^2 = 5/36)
member H = [(1, 0), (2/3, sqrt(5)/6), (-2/3, sqrt(5)/6), (-1, 0), (-2/3, -sqrt(5)/6), (2/3, -sqrt(5)/6)]
certified on ellipse and all sides tangent to the caustic: True
antipedal vertices w.r.t. f_1: [(1, (-2*sqrt(15) - sqrt(5))/10), (sqrt(3)/2, -sqrt(5)/5), (-1, (-sqrt(5) + 2*sqrt(15))/10), (-1, (-2*sqrt(15) + sqrt(5))/10), (sqrt(3)/2, sqrt(5)/5), (1, (sqrt(5) + 2*sqrt(15))/10)]
signed area of the antipedal polygon: 0
  A      = 5*sqrt(5)/9 = 1.24225998749988316467176314930
  Adag   = 15*sqrt(5)/2 = 16.7705098312484227230688025155
  Apol   = 32*sqrt(5) = 71.5541752799932702850935573994
  Adual  = 5*sqrt(5)/96 = 0.116461873828114046687977795246
  Aant   = 0 = 0
  Apol/Adag = 64/15   Apol/Adual = 3072/5
