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, 9/1, 10/1, 14/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-infinity,-1.146566) (-1.135428,-1.134818) (-1.131176,-1.129593) (-1.129069,-1.127420) (-1.125000,-1.117647) (-1.117152,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 (-1.147256,-1.145858) -133/116 HST (-1.146364,-1.146319) -47/41 EXTENDED HST (-1.145966,-1.145752) -982/857 HST (-1.145837,-1.145829) -55/48 EXTENDED HST (-1.146207,-1.145299) -173/151 HST (-1.145671,-1.145592) -118/103 HST (-1.145458,-1.145452) -63/55 EXTENDED HST (-1.145427,-1.144310) -71/62 HST (-1.146199,-1.142857) -119/104 HST (-1.143031,-1.142673) -8/7 EXTENDED HST (-1.143396,-1.140853) -153/134 HST (-1.141787,-1.141334) -129/113 HST (-1.141521,-1.140988) -105/92 HST (-1.141257,-1.140654) -81/71 HST (-1.140716,-1.140584) -665/583 HST (-1.140645,-1.139769) -57/50 HST (-1.139810,-1.138737) -49/43 EXTENDED HST -> HST (-1.139275,-1.137694) -33/29 EXTENDED HST -> HST (-1.137761,-1.137622) -661/581 HST (-1.137684,-1.137544) -124/109 HST (-1.137645,-1.137414) -397/349 HST (-1.137504,-1.137496) -91/80 EXTENDED HST (-1.137420,-1.137404) -985/866 HST (-1.137411,-1.137090) -58/51 HST (-1.137361,-1.136344) -83/73 HST (-1.136382,-1.136345) -25/22 EXTENDED HST (-1.136986,-1.134831) -67/59 HST (-1.134835,-1.134667) -261/230 HST (-1.134762,-1.134249) -59/52 HST (-1.134510,-1.134138) -169/149 HST (-1.134152,-1.133886) -93/82 HST (-1.134199,-1.133527) -144/127 HST (-1.133552,-1.133478) -399/352 HST (-1.133858,-1.133047) -535/472 HST (-1.133373,-1.133293) -17/15 EXTENDED HST (-1.133108,-1.132985) -264/233 HST (-1.133031,-1.132864) -213/188 HST (-1.132952,-1.132788) -162/143 HST (-1.132845,-1.131359) -43/38 EXTENDED HST -> HST (-1.131481,-1.131140) -112/99 HST (-1.129639,-1.129177) -96/85 HST (-1.129281,-1.129090) -507/449 HST (-1.129174,-1.129128) -271/240 HST (-1.129099,-1.129077) -656/581 HST (-1.129083,-1.129066) -831/736 HST (-1.128626,-1.125867) -62/55 HST (-1.126684,-1.124965) -170/151 HST (-1.125141,-1.124857) -9/8 EXTENDED HST (-1.117741,-1.117553) -19/17 EXTENDED HST (-1.118522,-1.115608) -143/128 HST The supplemental half-space computation shows that these NET maps are rational. SLOPE FUNCTION INFORMATION NUMBER OF FIXED POINTS: 1 EQUATOR? FIXED POINT c d 0 lambda1 lambda2 lambda1+lambda2 7/8 1 23 No Yes No Yes NUMBER OF EQUATORS: 0 1 0 1 There are no more slope function fixed points. Number of excluded intervals computed by the fixed point finder: 5024 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 either one of the above cycles or 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*b,b,b,1,1,1,1,1,1,1,1,1,b^-1,b^-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,a*b,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*b,c^-1*b,b,1,1,1,1,1,1,1,1,1,b^-1*c,b^-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)", "c=<1,a*b,a*b,a*b,a*b,a*b,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*d,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,a*b,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*b,c^-1*b,b,1,1,1,1,1,1,1,1,1,b^-1*c,b^-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)", "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");