--- N=3 member M1: a^2=8, b^2=3, lambda=72/25; on-ellipse residuals [0, 0, 0]; tangency residuals [0, 0, 0]
    polar = poles of sides: True
    polar sides tangent to circle (Op, a/b^2): [0, 0, 0]
    dualR vertices on circle (Op, b^2/a): [0, 0, 0]
    A        = 54*sqrt(6)/25   (~5.290897844411664692106134)
    Adag     = (sqrt(15) + 4*sqrt(6))/64   (~0.2136084737084395199682563)
    Apol     = (8*sqrt(15) + 32*sqrt(6))/3   (~36.45584617957367807458240)
    AdualR   = (27*sqrt(15) + 108*sqrt(6))/320   (~1.153485758025573407828584)
    AdualP   = (27*sqrt(15) + 108*sqrt(6))/1280   (~0.2883714395063933519571460)
    Aped     = (-24*sqrt(15) + 96*sqrt(6))/625   (~0.2275190639971313474922190)
    Aant     = -9*sqrt(15) + 36*sqrt(6)   (~53.32478062432765956848884)
    Aped_i   = 3*sqrt(6)/800   (~0.009185586535436917868239815)
    Aped_ii  = (8*sqrt(15) + 32*sqrt(6))/3   (~36.45584617957367807458240)
    k813        = 512/3   (~170.6666666666666666666667)
    k814R       = 2560/81   (~31.60493827160493827160494)
    k814P       = 10240/81   (~126.4197530864197530864198)
    k815_i_R    = 243*sqrt(10)/256000 + 243/32000   (~0.01059544324773795381904582)
    k815_i_P    = 243*sqrt(10)/1024000 + 243/128000   (~0.002648860811934488454761456)
    k815_ii_R   = 27*sqrt(10)/5 + 999/40   (~42.05129936490924839279403)
    k815_iii_R  = 6561/25000   (~0.2624400000000000000000000)
    k816_i_R    = (16 - 2*sqrt(10))/1215   (~0.007963328954455342663376307)
    k816_i_P    = (64 - 8*sqrt(10))/1215   (~0.03185331581782137065350523)
    k816_iii_R  = (18944 - 4096*sqrt(10))/30375   (~0.1972447968378705598726760)
    A_Adag      = 81*sqrt(10)/800 + 81/100   (~1.130180613092048407364888)
    Aant_over_A = 50/3 - 25*sqrt(10)/12   (~10.07858820798254305833564)
--- N=3 member M2: a^2=8, b^2=3, lambda=72/25; on-ellipse residuals [0, 0, 0]; tangency residuals [0, 0, 0]
    polar = poles of sides: True
    polar sides tangent to circle (Op, a/b^2): [0, 0, 0]
    dualR vertices on circle (Op, b^2/a): [0, 0, 0]
    A        = 144/25   (~5.760000000000000000000000)
    Adag     = 9/64   (~0.1406250000000000000000000)
    Apol     = 24   (~24.00000000000000000000000)
    AdualR   = 243/320   (~0.7593750000000000000000000)
    AdualP   = 243/1280   (~0.1898437500000000000000000)
    Aped     = 216/625   (~0.3456000000000000000000000)
    Aant     = 96   (~96.00000000000000000000000)
    Aped_i   = 27/3200   (~0.008437500000000000000000000)
    Aped_ii  = 24   (~24.00000000000000000000000)
    k813        = 512/3   (~170.6666666666666666666667)
    k814R       = 2560/81   (~31.60493827160493827160494)
    k814P       = 10240/81   (~126.4197530864197530864198)
    k815_i_R    = 6561/1024000   (~0.006407226562500000000000000)
    k815_i_P    = 6561/4096000   (~0.001601806640625000000000000)
    k815_ii_R   = 729/40   (~18.22500000000000000000000)
    k815_iii_R  = 6561/25000   (~0.2624400000000000000000000)
    k816_i_R    = 1/90   (~0.01111111111111111111111111)
    k816_i_P    = 2/45   (~0.04444444444444444444444444)
    k816_iii_R  = 512/1125   (~0.4551111111111111111111111)
    A_Adag      = 81/100   (~0.8100000000000000000000000)
    Aant_over_A = 50/3   (~16.66666666666666666666667)
N=3 differences (M1 - M2):
    k813       : 0
    k814R      : 0
    k814P      : 0
    k815_i_R   : 243/204800 + 243*sqrt(10)/256000
    k815_i_P   : 243/819200 + 243*sqrt(10)/1024000
    k815_ii_R  : 27/4 + 27*sqrt(10)/5
    k815_iii_R : 0
    k816_i_R   : 1/486 - 2*sqrt(10)/1215
    k816_i_P   : 2/243 - 8*sqrt(10)/1215
    k816_iii_R : 1024/6075 - 4096*sqrt(10)/30375
    A_Adag     : 81*sqrt(10)/800
    Aant_over_A: -25*sqrt(10)/12
--- N=4 rhombus R1: a^2=25, b^2=16, lambda=400/41; on-ellipse residuals [0, 0, 0, 0]; tangency residuals [0, 0, 0, 0]
    polar = poles of sides: True
    polar sides tangent to circle (Op, a/b^2): [0, 0, 0, 0]
    dualR vertices on circle (Op, b^2/a): [0, 0, 0, 0]
    A        = 40   (~40.00000000000000000000000)
    Adag     = 1/10   (~0.1000000000000000000000000)
    Apol     = 125/256   (~0.4882812500000000000000000)
    AdualR   = 2048/125   (~16.38400000000000000000000)
    AdualP   = 1024/125   (~8.192000000000000000000000)
    Aped     = 32000/1681   (~19.03628792385484830458061)
    Aant     = 80   (~80.00000000000000000000000)
    Aped_i   = 4096/210125   (~0.01949315883402736466389054)
    Aped_ii  = 125/256   (~0.4882812500000000000000000)
    k813        = 625/128   (~4.882812500000000000000000)
    k814R       = 15625/524288   (~0.02980232238769531250000000)
    k814P       = 15625/262144   (~0.05960464477539062500000000)
    k815_i_R    = 8388608/26265625   (~0.3193759143367043426531826)
    k815_i_P    = 4194304/26265625   (~0.1596879571683521713265913)
    k815_ii_R   = 8   (~8.000000000000000000000000)
    k815_iii_R  = 524288/1681   (~311.8905413444378346222487)
    k816_i_R    = 2/1681   (~0.001189767995240928019036288)
    k816_i_P    = 4/1681   (~0.002379535990481856038072576)
    k816_iii_R  = 15625/13448   (~1.161882807852468768590125)
    A_Adag      = 4   (~4.000000000000000000000000)
    Aant_over_A = 2   (~2.000000000000000000000000)
--- N=4 rectangle R2: a^2=25, b^2=16, lambda=400/41; on-ellipse residuals [0, 0, 0, 0]; tangency residuals [0, 0, 0, 0]
    polar = poles of sides: True
    polar sides tangent to circle (Op, a/b^2): [0, 0, 0, 0]
    dualR vertices on circle (Op, b^2/a): [0, 0, 0, 0]
    A        = 1600/41   (~39.02439024390243902439024)
    Adag     = 41/400   (~0.1025000000000000000000000)
    Apol     = 1025/2048   (~0.5004882812500000000000000)
    AdualR   = 10496/625   (~16.79360000000000000000000)
    AdualP   = 5248/625   (~8.396800000000000000000000)
    Aped     = 800/41   (~19.51219512195121951219512)
    Aant     = 3200/41   (~78.04878048780487804878049)
    Aped_i   = 328/15625   (~0.02099200000000000000000000)
    Aped_ii  = 1025/2048   (~0.5004882812500000000000000)
    k813        = 625/128   (~4.882812500000000000000000)
    k814R       = 15625/524288   (~0.02980232238769531250000000)
    k814P       = 15625/262144   (~0.05960464477539062500000000)
    k815_i_R    = 3442688/9765625   (~0.3525312512000000000000000)
    k815_i_P    = 1721344/9765625   (~0.1762656256000000000000000)
    k815_ii_R   = 1681/200   (~8.405000000000000000000000)
    k815_iii_R  = 8192/25   (~327.6800000000000000000000)
    k816_i_R    = 1/800   (~0.001250000000000000000000000)
    k816_i_P    = 1/400   (~0.002500000000000000000000000)
    k816_iii_R  = 15625/13448   (~1.161882807852468768590125)
    A_Adag      = 4   (~4.000000000000000000000000)
    Aant_over_A = 2   (~2.000000000000000000000000)
N=4 differences (R1 - R2):
    k813       : 0
    k814R      : 0
    k814P      : 0
    k815_i_R   : -544278528/16416015625
    k815_i_P   : -272139264/16416015625
    k815_ii_R  : -81/200
    k815_iii_R : -663552/42025
    k816_i_R   : -81/1344800
    k816_i_P   : -81/672400
    k816_iii_R : 0
    A_Adag     : 0
    Aant_over_A: 0
--- N=6 member H (b/a=1/2): a^2=1, b^2=1/4, lambda=1/9; on-ellipse residuals [0, 0, 0, 0, 0, 0]; tangency residuals [0, 0, 0, 0, 0, 0]
    polar = poles of sides: True
    polar sides tangent to circle (Op, a/b^2): [0, 0, 0, 0, 0, 0]
    dualR vertices on circle (Op, b^2/a): [0, 0, 0, 0, 0, 0]
    A        = 5*sqrt(5)/9   (~1.242259987499883164671763)
    Adag     = 15*sqrt(5)/2   (~16.77050983124842272306880)
    Apol     = 32*sqrt(5)   (~71.55417527999327028509356)
    AdualR   = 5*sqrt(5)/96   (~0.1164618738281140466879778)
    AdualP   = 25*sqrt(5)/768   (~0.07278867114257127917998612)
    Aped     = 50*sqrt(5)/81   (~1.380288874999870182968626)
    Aant     = 0   (~0)
    Aped_i   = 25*sqrt(5)/36   (~1.552824984374853955839704)
    Aped_ii  = 32*sqrt(5)   (~71.55417527999327028509356)
    k813        = 64/15   (~4.266666666666666666666667)
    k814R       = 3072/5   (~614.4000000000000000000000)
    k814P       = 24576/25   (~983.0400000000000000000000)
    k815_i_R    = 625/3456   (~0.1808449074074074074074074)
    k815_i_P    = 3125/27648   (~0.1130280671296296296296296)
    k815_ii_R   = 25/3   (~8.333333333333333333333333)
    k815_iii_R  = 625/3888   (~0.1607510288065843621399177)
    k816_i_R    = 40/3   (~13.33333333333333333333333)
    k816_i_P    = 64/3   (~21.33333333333333333333333)
    k816_iii_R  = 320/27   (~11.85185185185185185185185)
    A_Adag      = 125/6   (~20.83333333333333333333333)
    Aant_over_A = 0   (~0)
