These Thurston maps are NET maps for every choice of translation term. They are primitive and have degree 24. PURE MODULAR GROUP HURWITZ EQUIVALENCE CLASSES FOR TRANSLATIONS {0} {lambda1} {lambda2} {lambda1+lambda2} Since no Thurston multiplier is 1, this modular group Hurwitz class contains only finitely many Thurston equivalence classes. The number of pure modular group Hurwitz classes in this modular group Hurwitz class is 7. ALL THURSTON MULTIPLIERS c/d IN UNREDUCED FORM 0/24, 1/12, 1/8, 1/6, 1/4, 1/2, 3/6, 2/3, 4/3, 2/1, 5/2, 7/2, 11/2, 10/1 12/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-infinity,-1.156055) (-1.155645,-1.150676) (-1.147565,-1.146287) (-1.138506,-1.137600) (-1.135417,-1.134615) (-1.131718,-1.127957) (-1.124325,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 (-1.159949,-1.152143) -89/77 HST (-1.150850,-1.150574) -191/166 HST (-1.150692,-1.150452) -405/352 HST (-1.150541,-1.150534) -107/93 EXTENDED HST (-1.150466,-1.150421) -130/113 HST (-1.150595,-1.150264) -413/359 HST (-1.150407,-1.150406) -283/246 EXTENDED HST (-1.150397,-1.150357) -153/133 HST (-1.150273,-1.150246) -222/193 HST (-1.150414,-1.150037) -245/213 HST (-1.150073,-1.149926) -23/20 EXTENDED HST (-1.150000,-1.147727) -31/27 EXTENDED HST -> HST (-1.148069,-1.146982) -101/88 HST (-1.146465,-1.145570) -55/48 HST (-1.145742,-1.145006) -63/55 HST (-1.145077,-1.144858) -229/200 HST (-1.144937,-1.144422) -79/69 HST (-1.144483,-1.144087) -111/97 HST (-1.144192,-1.143871) -135/118 HST (-1.143912,-1.141913) -8/7 EXTENDED HST (-1.141947,-1.141696) -153/134 HST (-1.141776,-1.141482) -129/113 HST (-1.141526,-1.141170) -97/85 HST (-1.141221,-1.141026) -283/248 HST (-1.141125,-1.140677) -81/71 HST (-1.140713,-1.140619) -373/327 HST (-1.140632,-1.140618) -73/64 EXTENDED HST (-1.140625,-1.140411) -138/121 HST (-1.140522,-1.140306) -333/292 HST (-1.140379,-1.139775) -57/50 HST (-1.140357,-1.139416) -155/136 HST (-1.139555,-1.139537) -2311/2028 HST (-1.139546,-1.139524) -49/43 EXTENDED HST (-1.139709,-1.139133) -139/122 HST (-1.139344,-1.139175) -90/79 HST (-1.139180,-1.139020) -131/115 HST (-1.139223,-1.138873) -254/223 HST (-1.138957,-1.138000) -41/36 EXTENDED HST -> HST (-1.137823,-1.137458) -463/407 HST (-1.137592,-1.136177) -25/22 EXTENDED HST -> HST (-1.136249,-1.135504) -117/103 HST (-1.135858,-1.135732) -92/81 HST (-1.135599,-1.135587) -67/59 EXTENDED HST (-1.135723,-1.134931) -109/96 HST (-1.135189,-1.133602) -59/52 HST (-1.133993,-1.133124) -297/262 HST (-1.133423,-1.133238) -17/15 EXTENDED HST (-1.133775,-1.123886) -60/53 HST The supplemental half-space computation shows that these NET maps are rational. SLOPE FUNCTION INFORMATION NUMBER OF FIXED POINTS: 2 EQUATOR? FIXED POINT c d 0 lambda1 lambda2 lambda1+lambda2 7/8 2 3 No No No No 8/9 1 8 No No No No NUMBER OF EQUATORS: 0 0 0 0 There are no more slope function fixed points. Number of excluded intervals computed by the fixed point finder: 8333 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=(2,24)(3,23)(4,22)(5,21)(6,20)(7,19)(8,18)(9,17)(10,16)(11,15)(12,14)", "b=(1,24)(2,23)(3,22)(4,21)(5,20)(6,19)(7,18)(8,17)(9,16)(10,15)(11,14)(12,13)", "c=(1,24)(2,23)(3,22)(4,21)(5,20)(6,19)(7,18)(8,17)(9,16)(10,15)(11,14)(12,13)", "d=<1,a*b,a*b,a*b,a*b,a*b,1,1,1,1,1,1,1,1,1,1,1,1,1,c*d,c*d,c*d,c*d,c*d>(2,24)(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 lambda1: NewSphereMachine( "a=(1,2)(3,24)(4,23)(5,22)(6,21)(7,20)(8,19)(9,18)(10,17)(11,16)(12,15)(13,14)", "b=(2,24)(3,23)(4,22)(5,21)(6,20)(7,19)(8,18)(9,17)(10,16)(11,15)(12,14)", "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,c,c*d,c*d,c*d,c*d,c*d>(2,24)(3,23)(4,22)(5,21)(6,20)(7,19)(8,18)(9,17)(10,16)(11,15)(12,14)", "d=<1,1,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>(1,2)(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 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=(1,24)(2,23)(3,22)(4,21)(5,20)(6,19)(7,18)(8,17)(9,16)(10,15)(11,14)(12,13)", "c=(1,24)(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"); When the translation term of the affine map is lambda1+lambda2: NewSphereMachine( "a=(1,24)(2,23)(3,22)(4,21)(5,20)(6,19)(7,18)(8,17)(9,16)(10,15)(11,14)(12,13)", "b=<1,a*b,a*b,a*b,a*b,a*b,c^-1,1,1,1,1,1,1,1,1,1,1,1,c,c*d,c*d,c*d,c*d,c*d>(2,24)(3,23)(4,22)(5,21)(6,20)(7,19)(8,18)(9,17)(10,16)(11,15)(12,14)", "c=(2,24)(3,23)(4,22)(5,21)(6,20)(7,19)(8,18)(9,17)(10,16)(11,15)(12,14)", "d=(1,24)(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");