These Thurston maps are NET maps for every choice of translation term. They are primitive and have degree 28. 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 0/7, 0/14, 0/28, 1/28, 1/4, 2/7, 2/4, 3/4, 2/2, 2/1, 6/2, 4/1, 6/1, 8/1 10/1, 12/1, 16/1, 20/1, 22/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-infinity,-1.200568) (-1.199149,-1.188618) (-1.186520,-1.180609) (-1.174942,-1.172795) (-1.171852,-1.170919) (-1.163104,-1.161171) (-1.160958,-1.159138) (-1.156974,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 (-1.201132,-1.198940) -6/5 EXTENDED HST (-1.190000,-1.187500) -82/69 HST (-1.187580,-1.187421) -19/16 EXTENDED HST (-1.187898,-1.186486) -203/171 HST (-1.187123,-1.186248) -89/75 HST (-1.181003,-1.179828) -59/50 HST (-1.180431,-1.179179) -105/89 HST (-1.179505,-1.179470) -46/39 EXTENDED HST (-1.179237,-1.178984) -79/67 HST (-1.180152,-1.177940) -112/95 HST (-1.178614,-1.178528) -33/28 EXTENDED HST (-1.178532,-1.176830) -53/45 HST (-1.176838,-1.176822) -6156/5231 HST (-1.176830,-1.176829) -193/164 EXTENDED HST (-1.176829,-1.176080) -20/17 EXTENDED HST (-1.176412,-1.175520) -127/108 HST (-1.175846,-1.175801) -107/91 HST (-1.175677,-1.175674) -87/74 EXTENDED HST (-1.175545,-1.175473) -288/245 HST (-1.175494,-1.175377) -67/57 HST (-1.175407,-1.175337) -315/268 HST (-1.175373,-1.175000) -114/97 HST (-1.175172,-1.174353) -47/40 EXTENDED HST -> HST (-1.172846,-1.172475) -129/110 HST (-1.172590,-1.171402) -34/29 EXTENDED HST -> HST (-1.170944,-1.170762) -185/158 HST (-1.170800,-1.169602) -48/41 EXTENDED HST -> HST (-1.169740,-1.169192) -69/59 HST (-1.169337,-1.168661) -83/71 HST (-1.168684,-1.168139) -104/89 HST (-1.168259,-1.167857) -139/119 HST (-1.168001,-1.167650) -167/143 HST (-1.167778,-1.165570) -7/6 EXTENDED HST (-1.165622,-1.165216) -155/133 HST (-1.165384,-1.164907) -127/109 HST (-1.165051,-1.164371) -106/91 HST (-1.164719,-1.164079) -92/79 HST (-1.164402,-1.163487) -71/61 HST (-1.163690,-1.162899) -57/49 HST (-1.161339,-1.160490) -137/118 HST (-1.159591,-1.157777) -51/44 HST (-1.158803,-1.154879) -22/19 EXTENDED HST -> 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 6/7 1 4 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: 6494 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=(2,28)(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=(1,28)(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=(1,28)(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,a*b,a*b,a*b,a*b,a*b,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c,c*d,c*d,c*d,c*d,c*d>(2,28)(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 lambda1: NewSphereMachine( "a=(1,2)(3,28)(4,27)(5,26)(6,25)(7,24)(8,23)(9,22)(10,21)(11,20)(12,19)(13,18)(14,17)(15,16)", "b=(2,28)(3,27)(4,26)(5,25)(6,24)(7,23)(8,22)(9,21)(10,20)(11,19)(12,18)(13,17)(14,16)", "c=<1,a*b,a*b,a*b,a*b,a*b,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,c,c,c*d,c*d,c*d,c*d,c*d>(2,28)(3,27)(4,26)(5,25)(6,24)(7,23)(8,22)(9,21)(10,20)(11,19)(12,18)(13,17)(14,16)", "d=<1,1,a*b,a*b,a*b,a*b,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c,c*d,c*d,c*d,c*d,c*d>(1,2)(3,28)(4,27)(5,26)(6,25)(7,24)(8,23)(9,22)(10,21)(11,20)(12,19)(13,18)(14,17)(15,16)", "a*b*c*d"); When the translation term of the affine map is 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=(1,28)(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=(1,28)(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"); When the translation term of the affine map is lambda1+lambda2: NewSphereMachine( "a=(1,28)(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,a*b,a*b,a*b,a*b,a*b,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,c,c,c*d,c*d,c*d,c*d,c*d>(2,28)(3,27)(4,26)(5,25)(6,24)(7,23)(8,22)(9,21)(10,20)(11,19)(12,18)(13,17)(14,16)", "c=(2,28)(3,27)(4,26)(5,25)(6,24)(7,23)(8,22)(9,21)(10,20)(11,19)(12,18)(13,17)(14,16)", "d=(1,28)(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");