These Thurston maps are NET maps for every choice of translation term. They are primitive and have degree 23. PURE MODULAR GROUP HURWITZ EQUIVALENCE CLASSES FOR TRANSLATIONS {0} {lambda1} {lambda2} {lambda1+lambda2} These pure modular group Hurwitz classes each contain infinitely many Thurston equivalence classes. The number of pure modular group Hurwitz classes in this modular group Hurwitz class is 24. ALL THURSTON MULTIPLIERS c/d IN UNREDUCED FORM 0/23, 1/23, 1/1, 2/1, 3/1, 4/1, 5/1, 7/1, 8/1, 10/1, 15/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-infinity,-1.257843) (-1.257317,-1.256977) (-1.253460,-1.234079) (-1.231929,-1.229451) (-1.226440,-1.225138) (-1.222222,-1.193329) (-1.189357,-1.189049) (-1.187829,-1.167393) (-1.163837,-1.125936) (-1.125000,-1.000000) (-1.000000,infinity ) The half-space computation does not determine rationality. EXCLUDED INTERVALS FOR JUST THE SUPPLEMENTAL HALF-SPACE COMPUTATION INTERVAL COMPUTED FOR HST OR EXTENDED HST (-1.258399,-1.257302) -83/66 HST (-1.257532,-1.255736) -93/74 HST (-1.256416,-1.256404) -49/39 EXTENDED HST (-1.255961,-1.255362) -221/176 HST (-1.255641,-1.255638) -167/133 EXTENDED HST (-1.255628,-1.253812) -59/47 HST (-1.254078,-1.253522) -247/197 HST (-1.253778,-1.253685) -84/67 HST (-1.254022,-1.252914) -89/71 HST (-1.234321,-1.233754) -58/47 HST (-1.233771,-1.233516) -132/107 HST (-1.233541,-1.233419) -243/197 HST (-1.233449,-1.233381) -502/407 HST (-1.233400,-1.233361) -872/707 HST (-1.233449,-1.233271) -1501/1217 HST (-1.233353,-1.233313) -37/30 EXTENDED HST (-1.234602,-1.228749) -53/43 HST (-1.228779,-1.228620) -231/188 HST (-1.228737,-1.228496) -747/608 HST (-1.228594,-1.228549) -43/35 EXTENDED HST (-1.229667,-1.227318) -457/372 HST (-1.228488,-1.228203) -199/162 HST (-1.228386,-1.227745) -70/57 HST (-1.227905,-1.227537) -97/79 HST (-1.227848,-1.225352) -27/22 EXTENDED HST -> HST (-1.225239,-1.225022) -1121/915 HST (-1.225136,-1.223916) -49/40 EXTENDED HST -> HST (-1.224318,-1.223480) -82/67 HST (-1.224719,-1.222222) -115/94 HST (-1.222560,-1.221888) -11/9 EXTENDED HST (-1.193573,-1.192417) -68/57 HST (-1.192500,-1.192325) -440/369 HST (-1.192361,-1.192254) -31/26 EXTENDED HST (-1.192345,-1.191967) -335/281 HST (-1.192168,-1.190846) -56/47 HST (-1.191073,-1.190611) -156/131 HST (-1.190730,-1.190471) -431/362 HST (-1.190538,-1.190415) -25/21 EXTENDED HST (-1.191176,-1.187500) -69/58 HST (-1.167434,-1.167351) -1876/1607 HST (-1.167391,-1.167391) -537/460 EXTENDED HST (-1.167386,-1.167378) -272/233 HST (-1.167618,-1.167069) -286/245 HST (-1.167260,-1.166052) -7/6 EXTENDED HST (-1.166186,-1.165460) -232/199 HST (-1.165828,-1.164598) -141/121 HST (-1.165285,-1.162957) -71/61 HST (-1.126300,-1.125545) -152/135 HST (-1.125564,-1.124431) -9/8 EXTENDED HST (-1.008904,-0.990030) -1/1 EXTENDED HST The supplemental half-space computation shows that these NET maps are rational. SLOPE FUNCTION INFORMATION There are no slope function fixed points because every loop multiplier of the mod 2 slope correspondence graph is at least 1 and the map is rational. No nontrivial cycles were found. The slope function maps some slope to the nonslope. The slope function orbit of every slope p/q with |p| <= 50 and |q| <= 50 ends in the nonslope. FUNDAMENTAL GROUP WREATH RECURSIONS When the translation term of the affine map is 0: NewSphereMachine( "a=<1,b,c^-1*b,c^-1*b,c^-1*b,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,c,b^-1*c,b^-1*c,b^-1*c,b^-1*c>(2,23)(3,22)(4,21)(5,20)(6,19)(7,18)(8,17)(9,16)(10,15)(11,14)(12,13)", "b=(1,23)(2,22)(3,21)(4,20)(5,19)(6,18)(7,17)(8,16)(9,15)(10,14)(11,13)", "c=(1,23)(2,22)(3,21)(4,20)(5,19)(6,18)(7,17)(8,16)(9,15)(10,14)(11,13)", "d=<1,a*b,a*b,a*b,a*b,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,c*d,c*d,c*d,c*d,c*d>(2,23)(3,22)(4,21)(5,20)(6,19)(7,18)(8,17)(9,16)(10,15)(11,14)(12,13)", "a*b*c*d"); When the translation term of the affine map is lambda1: NewSphereMachine( "a=(1,2)(3,23)(4,22)(5,21)(6,20)(7,19)(8,18)(9,17)(10,16)(11,15)(12,14)", "b=<1,b,c^-1*b,c^-1*b,c^-1*b,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,c,c,b^-1*c,b^-1*c,b^-1*c,b^-1*c>(2,23)(3,22)(4,21)(5,20)(6,19)(7,18)(8,17)(9,16)(10,15)(11,14)(12,13)", "c=<1,a*b,a*b,a*b,a*b,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,c,c*d,c*d,c*d,c*d,c*d>(2,23)(3,22)(4,21)(5,20)(6,19)(7,18)(8,17)(9,16)(10,15)(11,14)(12,13)", "d=<1,1,a*b,a*b,a*b,a*b,c^-1,1,1,1,1,1,1,1,1,1,1,1,c,c*d,c*d,c*d,c*d>(1,2)(3,23)(4,22)(5,21)(6,20)(7,19)(8,18)(9,17)(10,16)(11,15)(12,14)", "a*b*c*d"); When the translation term of the affine map is lambda2: NewSphereMachine( "a=(1,22)(2,21)(3,20)(4,19)(5,18)(6,17)(7,16)(8,15)(9,14)(10,13)(11,12)", "b=(1,23)(2,22)(3,21)(4,20)(5,19)(6,18)(7,17)(8,16)(9,15)(10,14)(11,13)", "c=(1,23)(2,22)(3,21)(4,20)(5,19)(6,18)(7,17)(8,16)(9,15)(10,14)(11,13)", "d=(1,22)(2,21)(3,20)(4,19)(5,18)(6,17)(7,16)(8,15)(9,14)(10,13)(11,12)", "a*b*c*d"); When the translation term of the affine map is lambda1+lambda2: NewSphereMachine( "a=(1,23)(2,22)(3,21)(4,20)(5,19)(6,18)(7,17)(8,16)(9,15)(10,14)(11,13)", "b=<1,a*b,a*b,a*b,a*b,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,c,c*d,c*d,c*d,c*d,c*d>(2,23)(3,22)(4,21)(5,20)(6,19)(7,18)(8,17)(9,16)(10,15)(11,14)(12,13)", "c=<1,b,c^-1*b,c^-1*b,c^-1*b,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,c,c,b^-1*c,b^-1*c,b^-1*c,b^-1*c>(2,23)(3,22)(4,21)(5,20)(6,19)(7,18)(8,17)(9,16)(10,15)(11,14)(12,13)", "d=(1,23)(2,22)(3,21)(4,20)(5,19)(6,18)(7,17)(8,16)(9,15)(10,14)(11,13)", "a*b*c*d");