These Thurston maps are NET maps for every choice of translation term. They are primitive and have degree 16. 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 0/1, 0/4, 0/8, 0/16, 2/2, 2/1, 4/1, 6/1, 8/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-infinity,-1.000000) (-1.000000,-0.250000) (-0.250000,-0.159091) ( 0.152174,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 (-1.009009,-0.991150) -1/1 EXTENDED HST (-0.252336,-0.247649) -1/4 EXTENDED HST (-0.173077,-0.140000) -2/13 EXTENDED HST -> HST (-0.150000,-0.120690) -1/7 EXTENDED HST -> HST (-0.132353,-0.106061) -3/25 EXTENDED HST -> HST (-0.118421,-0.094595) -1/9 EXTENDED HST -> HST (-0.111099,0.142897 ) 0/1 EXTENDED HST ( 0.142857,0.142938 ) 512/3583 HST ( 0.142857,0.143022 ) 252/1763 HST ( 0.142857,0.143198 ) 124/867 HST ( 0.142857,0.143590 ) 60/419 HST ( 0.142857,0.144578 ) 28/195 HST ( 0.142857,0.148148 ) 12/83 HST ( 0.129630,0.173077 ) 4/27 EXTENDED HST -> HST The supplemental half-space computation shows that these NET maps are rational. SLOPE FUNCTION INFORMATION There are no slope function fixed points because every nonzero multiplier is at least 1 and the map is rational. Similarly, there are not even any slope function cycles. 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 the nonslope. If the slope function maps slope p/q to slope p'/q', then |p'| <= |p| for every slope p/q with |p| <= 50 and |q| <= 50. 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,b,c^-1*b,c^-1,1,1,1,1,1,1,1,c,b^-1*c,b^-1,b^-1>(2,16)(3,15)(4,14)(5,13)(6,12)(7,11)(8,10)", "b=(1,16)(2,15)(3,14)(4,13)(5,12)(6,11)(7,10)(8,9)", "c=(1,16)(2,15)(3,14)(4,13)(5,12)(6,11)(7,10)(8,9)", "d=<1,a*b,a*b,c^-1,c^-1,1,1,1,1,1,1,1,c,c,c*d,c*d>(2,16)(3,15)(4,14)(5,13)(6,12)(7,11)(8,10)", "a*b*c*d"); When the translation term of the affine map is lambda1: NewSphereMachine( "a=(1,2)(3,16)(4,15)(5,14)(6,13)(7,12)(8,11)(9,10)", "b=<1,b,b,c^-1*b,c^-1,c^-1,1,1,1,1,1,c,c,b^-1*c,b^-1,b^-1>(2,16)(3,15)(4,14)(5,13)(6,12)(7,11)(8,10)", "c=<1,a*b,a*b,c^-1,c^-1,c^-1,1,1,1,1,1,c,c,c,c*d,c*d>(2,16)(3,15)(4,14)(5,13)(6,12)(7,11)(8,10)", "d=<1,1,a*b,c^-1,c^-1,c^-1,1,1,1,1,1,1,c,c,c*d,c*d>(1,2)(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 lambda2: NewSphereMachine( "a=(1,15)(2,14)(3,13)(4,12)(5,11)(6,10)(7,9)", "b=(1,16)(2,15)(3,14)(4,13)(5,12)(6,11)(7,10)(8,9)", "c=(1,16)(2,15)(3,14)(4,13)(5,12)(6,11)(7,10)(8,9)", "d=(1,15)(2,14)(3,13)(4,12)(5,11)(6,10)(7,9)", "a*b*c*d"); When the translation term of the affine map is lambda1+lambda2: NewSphereMachine( "a=(1,16)(2,15)(3,14)(4,13)(5,12)(6,11)(7,10)(8,9)", "b=<1,a*b,a*b,c^-1,c^-1,c^-1,1,1,1,1,1,c,c,c,c*d,c*d>(2,16)(3,15)(4,14)(5,13)(6,12)(7,11)(8,10)", "c=<1,b,b,c^-1*b,c^-1,c^-1,1,1,1,1,1,c,c,b^-1*c,b^-1,b^-1>(2,16)(3,15)(4,14)(5,13)(6,12)(7,11)(8,10)", "d=(1,16)(2,15)(3,14)(4,13)(5,12)(6,11)(7,10)(8,9)", "a*b*c*d");