These Thurston maps are NET maps for every choice of translation term. They are primitive and have degree 19. 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 0/1, 0/19, 1/19, 1/1, 2/1, 3/1, 4/1, 6/1, 7/1, 9/1, 10/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-infinity,-1.015729) (-0.984751,-0.015800) ( 0.015653,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 (-1.022556,-1.007752) -65/64 HST (-1.009458,-1.006067) -130/129 HST (-1.007386,-1.004741) -166/165 HST (-1.005776,-0.994290) -1/1 EXTENDED HST (-0.995063,-0.992360) -157/158 HST (-0.993631,-0.993630) -156/157 EXTENDED HST (-0.993590,-0.993589) -155/156 EXTENDED HST (-0.993549,-0.993548) -154/155 EXTENDED HST (-0.993507,-0.993506) -153/154 EXTENDED HST (-0.993500,-0.989960) -119/120 HST (-0.991597,-0.991596) -118/119 EXTENDED HST (-0.991526,-0.991525) -117/118 EXTENDED HST (-0.991454,-0.991452) -116/117 EXTENDED HST (-0.991380,-0.991378) -115/116 EXTENDED HST (-0.991348,-0.978046) -65/66 HST (-0.186555,0.297848 ) 0/1 EXTENDED 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 1/1 1 19 No Yes Yes No NUMBER OF EQUATORS: 0 1 1 0 There are no more slope function fixed points. Number of excluded intervals computed by the fixed point finder: 3459 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,b,c^-1*b,c^-1*b,c^-1*b,b,b,1,1,1,1,1,1,1,b^-1,b^-1*c,b^-1*c,b^-1*c,b^-1>(2,19)(3,18)(4,17)(5,16)(6,15)(7,14)(8,13)(9,12)(10,11)", "b=(1,19)(2,18)(3,17)(4,16)(5,15)(6,14)(7,13)(8,12)(9,11)", "c=(1,19)(2,18)(3,17)(4,16)(5,15)(6,14)(7,13)(8,12)(9,11)", "d=<1,a*b,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,c,c,c,c*d>(2,19)(3,18)(4,17)(5,16)(6,15)(7,14)(8,13)(9,12)(10,11)", "a*b*c*d"); When the translation term of the affine map is lambda1: NewSphereMachine( "a=(1,2)(3,19)(4,18)(5,17)(6,16)(7,15)(8,14)(9,13)(10,12)", "b=<1,b,c^-1*b,c^-1*b,c^-1*b,c^-1*b,b,1,1,1,1,1,1,1,b^-1*c,b^-1*c,b^-1*c,b^-1*c,b^-1>(2,19)(3,18)(4,17)(5,16)(6,15)(7,14)(8,13)(9,12)(10,11)", "c=<1,a*b,c^-1,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,c,c,c,c,c*d>(2,19)(3,18)(4,17)(5,16)(6,15)(7,14)(8,13)(9,12)(10,11)", "d=<1,1,c^-1,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,1,c,c,c,c*d>(1,2)(3,19)(4,18)(5,17)(6,16)(7,15)(8,14)(9,13)(10,12)", "a*b*c*d"); When the translation term of the affine map is lambda2: NewSphereMachine( "a=(1,18)(2,17)(3,16)(4,15)(5,14)(6,13)(7,12)(8,11)(9,10)", "b=(1,19)(2,18)(3,17)(4,16)(5,15)(6,14)(7,13)(8,12)(9,11)", "c=(1,19)(2,18)(3,17)(4,16)(5,15)(6,14)(7,13)(8,12)(9,11)", "d=(1,18)(2,17)(3,16)(4,15)(5,14)(6,13)(7,12)(8,11)(9,10)", "a*b*c*d"); When the translation term of the affine map is lambda1+lambda2: NewSphereMachine( "a=(1,19)(2,18)(3,17)(4,16)(5,15)(6,14)(7,13)(8,12)(9,11)", "b=<1,a*b,c^-1,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,c,c,c,c,c*d>(2,19)(3,18)(4,17)(5,16)(6,15)(7,14)(8,13)(9,12)(10,11)", "c=<1,b,c^-1*b,c^-1*b,c^-1*b,c^-1*b,b,1,1,1,1,1,1,1,b^-1*c,b^-1*c,b^-1*c,b^-1*c,b^-1>(2,19)(3,18)(4,17)(5,16)(6,15)(7,14)(8,13)(9,12)(10,11)", "d=(1,19)(2,18)(3,17)(4,16)(5,15)(6,14)(7,13)(8,12)(9,11)", "a*b*c*d");