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 infinitely many Thurston equivalence classes. The number of pure modular group Hurwitz classes in this modular group Hurwitz class is 12. ALL THURSTON MULTIPLIERS c/d IN UNREDUCED FORM 0/9, 0/27, 1/9, 1/3, 2/3, 1/1, 2/1, 3/1, 4/1, 6/1, 7/1, 8/1, 10/1, 11/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-infinity,-0.680540) (-0.672789,-0.509434) (-0.491525,-0.430108) (-0.430025,-0.400000) (-0.397163,-0.381273) (-0.380952,-0.349219) (-0.317726,-0.274619) (-0.272109,-0.269504) (-0.269318,-0.245450) (-0.244716,-0.122807) (-0.122197,-0.014184) ( 0.013605,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 (-0.683983,-0.675105) -17/25 EXTENDED HST -> HST (-0.675676,-0.673913) -27/40 EXTENDED HST -> HST (-0.676190,-0.671362) -31/46 EXTENDED HST -> HST (-0.516016,-0.502677) -27/53 HST (-0.506634,-0.493537) -1/2 EXTENDED HST (-0.495413,-0.491379) -36/73 HST (-0.492997,-0.490358) -29/59 HST (-0.431652,-0.429424) -40/93 HST (-0.400848,-0.399137) -2/5 EXTENDED HST (-0.399267,-0.398551) -73/183 HST (-0.398907,-0.397849) -47/118 HST (-0.398268,-0.396624) -29/73 HST (-0.381457,-0.381016) -61/160 HST (-0.381194,-0.380709) -8/21 EXTENDED HST (-0.349634,-0.344732) -8/23 EXTENDED HST -> HST (-0.345675,-0.341001) -11/32 EXTENDED HST -> HST (-0.341238,-0.340303) -15/44 EXTENDED HST -> HST (-0.341432,-0.338221) -17/50 EXTENDED HST -> HST (-0.338956,-0.327893) -1/3 EXTENDED HST (-0.329152,-0.319609) -12/37 EXTENDED HST -> HST (-0.324124,-0.320415) -10/31 EXTENDED HST -> HST (-0.321629,-0.313399) -7/22 EXTENDED HST -> HST (-0.277636,-0.270602) -14/51 HST (-0.272943,-0.272510) -3/11 EXTENDED HST (-0.269697,-0.269113) -38/141 HST (-0.245955,-0.244224) -12/49 EXTENDED HST -> HST (-0.126437,-0.119048) -7/57 HST (-0.019048,-0.009804) -1/71 HST (-0.011905,0.012821 ) 0/1 EXTENDED HST ( 0.008772,0.018018 ) 1/74 HST The supplemental half-space computation shows that these NET maps are rational. SLOPE FUNCTION INFORMATION NUMBER OF FIXED POINTS FOUND: 1 EQUATOR? FIXED POINT c d 0 lambda1 lambda2 lambda1+lambda2 3/1 1 9 No No No No NUMBER OF EQUATORS FOUND: 0 0 0 0 Number of excluded intervals computed by the fixed point finder: 32785 The union of the excluded intervals computed by the fixed point finder became a union of 10,000 disjoint intervals: the search for all slope function fixed points aborted. 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. If the slope function maps slope p/q to slope p'/q', then |q'| <= |q| for every slope p/q with |p| <= 50 and |q| <= 50. FUNDAMENTAL GROUP WREATH RECURSIONS When the translation term of the affine map is 0: 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=(1,26)(2,25)(3,24)(4,23)(5,22)(6,21)(7,20)(8,19)(9,18)(10,17)(11,16)(12,15)(13,14)", "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=(1,27)(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: NewSphereMachine( "a=<1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,c,c,c,c,c,c,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)", "b=<1,a*b,b,c^-1*b,c^-1,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,c,c,c,c,c,b^-1*c,b^-1>(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=(1,27)(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=(1,27)(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 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=(1,27)(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=(1,26)(2,25)(3,24)(4,23)(5,22)(6,21)(7,20)(8,19)(9,18)(10,17)(11,16)(12,15)(13,14)", "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=(1,27)(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,a*b,b,c^-1*b,c^-1,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,c,c,c,c,c,b^-1*c,b^-1>(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,b*c*a*b,c^-1*b*c*b,c^-1*b,c^-1,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,c,c,c,c,b^-1*c,b^-1*d*a*c,c*d^2*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)", "a*b*c*d"); ****************************INTEGER OVERFLOW REPORT***************************** Imminent integer overflow caused the modular group computation to abort.