These Thurston maps are NET maps for every choice of translation term. They are primitive and have degree 27. PURE MODULAR GROUP HURWITZ EQUIVALENCE CLASSES FOR TRANSLATIONS {0} {lambda1} {lambda2} {lambda1+lambda2} These pure modular group Hurwitz classes each contain only finitely many Thurston equivalence classes. However, this modular group Hurwitz class contains 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 0/3, 0/9, 0/27, 1/27, 1/9, 2/9, 1/3, 2/3, 1/1, 3/3, 5/3, 2/1, 3/1, 4/1, 5/1 6/1, 7/1, 8/1, 9/1, 11/1, 14/1, 18/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-infinity,-1.115852) (-1.115789,-1.113043) (-1.108553,-1.107707) (-1.106383,-1.104478) (-1.102697,-1.102444) (-1.099620,-1.092696) (-1.091949,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 (-1.117117,-1.114504) -106/95 HST (-1.113965,-1.111991) -69/62 HST (-1.112710,-1.111111) -149/134 HST (-1.111295,-1.111236) -799/719 HST (-1.111266,-1.110961) -10/9 EXTENDED HST (-1.111695,-1.109840) -351/316 HST (-1.110759,-1.110584) -281/253 HST (-1.110664,-1.110440) -221/199 HST (-1.110540,-1.109920) -141/127 HST (-1.110176,-1.109570) -101/91 HST (-1.109890,-1.109091) -91/82 HST (-1.109689,-1.107887) -51/46 HST (-1.107769,-1.107617) -72/65 EXTENDED HST (-1.107686,-1.107374) -103/93 HST (-1.107386,-1.107249) -196/177 HST (-1.107276,-1.107201) -382/345 HST (-1.107234,-1.107161) -692/625 HST (-1.107194,-1.107153) -1250/1129 HST (-1.107174,-1.107112) -31/28 EXTENDED HST (-1.107143,-1.106742) -176/159 HST (-1.106881,-1.106859) -145/131 HST (-1.106842,-1.106500) -114/103 HST (-1.106672,-1.105737) -52/47 HST (-1.104778,-1.103934) -74/67 HST (-1.104310,-1.103466) -85/77 HST (-1.103469,-1.103428) -32/29 EXTENDED HST (-1.103494,-1.103264) -555/503 HST (-1.103378,-1.103310) -395/358 HST (-1.103345,-1.103298) -299/271 HST (-1.103306,-1.102855) -139/126 HST (-1.103160,-1.102751) -75/68 HST (-1.102822,-1.102615) -161/146 HST (-1.104167,-1.100000) -54/49 HST (-1.100294,-1.099689) -11/10 EXTENDED HST (-1.099808,-1.099448) -298/271 HST (-1.093064,-1.091515) -59/54 HST The supplemental half-space computation shows that these NET maps are rational. SLOPE FUNCTION INFORMATION There are no slope function fixed points. Number of excluded intervals computed by the fixed point finder: 4389 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=(2,27)(3,26)(4,25)(5,24)(6,23)(7,22)(8,21)(9,20)(10,19)(11,18)(12,17)(13,16)(14,15)", "b=(1,27)(2,26)(3,25)(4,24)(5,23)(6,22)(7,21)(8,20)(9,19)(10,18)(11,17)(12,16)(13,15)", "c=(1,27)(2,26)(3,25)(4,24)(5,23)(6,22)(7,21)(8,20)(9,19)(10,18)(11,17)(12,16)(13,15)", "d=<1,a*b,a*b,a*b,a*b,a*b,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c*d,c*d,c*d,c*d,c*d,c*d>(2,27)(3,26)(4,25)(5,24)(6,23)(7,22)(8,21)(9,20)(10,19)(11,18)(12,17)(13,16)(14,15)", "a*b*c*d"); When the translation term of the affine map is lambda1: NewSphereMachine( "a=(1,2)(3,27)(4,26)(5,25)(6,24)(7,23)(8,22)(9,21)(10,20)(11,19)(12,18)(13,17)(14,16)", "b=(2,27)(3,26)(4,25)(5,24)(6,23)(7,22)(8,21)(9,20)(10,19)(11,18)(12,17)(13,16)(14,15)", "c=<1,a*b,a*b,a*b,a*b,a*b,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c*d,c*d,c*d,c*d,c*d,c*d>(2,27)(3,26)(4,25)(5,24)(6,23)(7,22)(8,21)(9,20)(10,19)(11,18)(12,17)(13,16)(14,15)", "d=<1,1,a*b,a*b,a*b,a*b,a*b,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c*d,c*d,c*d,c*d,c*d>(1,2)(3,27)(4,26)(5,25)(6,24)(7,23)(8,22)(9,21)(10,20)(11,19)(12,18)(13,17)(14,16)", "a*b*c*d"); When the translation term of the affine map is lambda2: NewSphereMachine( "a=(1,26)(2,25)(3,24)(4,23)(5,22)(6,21)(7,20)(8,19)(9,18)(10,17)(11,16)(12,15)(13,14)", "b=(1,27)(2,26)(3,25)(4,24)(5,23)(6,22)(7,21)(8,20)(9,19)(10,18)(11,17)(12,16)(13,15)", "c=(1,27)(2,26)(3,25)(4,24)(5,23)(6,22)(7,21)(8,20)(9,19)(10,18)(11,17)(12,16)(13,15)", "d=(1,26)(2,25)(3,24)(4,23)(5,22)(6,21)(7,20)(8,19)(9,18)(10,17)(11,16)(12,15)(13,14)", "a*b*c*d"); When the translation term of the affine map is lambda1+lambda2: NewSphereMachine( "a=(1,27)(2,26)(3,25)(4,24)(5,23)(6,22)(7,21)(8,20)(9,19)(10,18)(11,17)(12,16)(13,15)", "b=<1,a*b,a*b,a*b,a*b,a*b,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c*d,c*d,c*d,c*d,c*d,c*d>(2,27)(3,26)(4,25)(5,24)(6,23)(7,22)(8,21)(9,20)(10,19)(11,18)(12,17)(13,16)(14,15)", "c=(2,27)(3,26)(4,25)(5,24)(6,23)(7,22)(8,21)(9,20)(10,19)(11,18)(12,17)(13,16)(14,15)", "d=(1,27)(2,26)(3,25)(4,24)(5,23)(6,22)(7,21)(8,20)(9,19)(10,18)(11,17)(12,16)(13,15)", "a*b*c*d");