These Thurston maps are NET maps for every choice of translation term. They are primitive and have degree 14. PURE MODULAR GROUP HURWITZ EQUIVALENCE CLASSES FOR TRANSLATIONS {0} {lambda1} {lambda2} {lambda1+lambda2} These pure modular group Hurwitz classes each contain only finitely many Thurston equivalence classes. However, this modular group Hurwitz class contains 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, 1/14, 1/7, 1/2, 1/1, 2/2, 3/2, 4/2, 3/1, 4/1, 5/1, 8/1, 11/1 12/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-infinity,-0.104964) (-0.103711,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 (-0.105263,-0.104712) -11/105 HST (-0.104724,-0.104612) -9/86 HST (-0.104623,-0.104608) -59/564 HST (-0.104610,-0.104606) -849/8116 HST (-0.104608,-0.104607) -84/803 HST (-0.104608,-0.104604) -134/1281 HST (-0.104604,-0.104603) -459/4388 HST (-0.104603,-0.104602) -25/239 EXTENDED HST (-0.104603,-0.104587) -41/392 HST (-0.104588,-0.104565) -16/153 HST (-0.104567,-0.104559) -55/526 HST (-0.104560,-0.104558) -250/2391 HST (-0.104558,-0.104557) -39/373 EXTENDED HST (-0.104558,-0.104556) -335/3204 HST (-0.104557,-0.104555) -140/1339 HST (-0.104555,-0.104551) -62/593 HST (-0.104555,-0.104544) -108/1033 HST (-0.104548,-0.104543) -23/220 EXTENDED HST (-0.104547,-0.104527) -99/947 HST (-0.104540,-0.104522) -30/287 HST (-0.104523,-0.104517) -37/354 HST (-0.104540,-0.104475) -44/421 HST (-0.104486,-0.104469) -7/67 EXTENDED HST (-0.104488,-0.104423) -117/1120 HST (-0.104464,-0.104385) -40/383 HST (-0.104433,-0.104014) -19/182 HST (-0.104365,-0.104324) -12/115 HST (-0.104213,-0.104112) -5/48 EXTENDED HST (-0.104087,-0.103996) -13/125 HST (-0.104006,-0.103970) -73/702 HST (-0.103988,-0.103963) -47/452 HST (-0.103979,-0.103683) -8/77 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 loop multiplier of the mod 2 slope correspondence graph is at least 1 and the map is rational. 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 the nonslope. FUNDAMENTAL GROUP WREATH RECURSIONS When the translation term of the affine map is 0: NewSphereMachine( "a=(1,13)(2,12)(3,11)(4,10)(5,9)(6,8)", "b=(1,13)(2,12)(3,11)(4,10)(5,9)(6,8)", "c=(1,14)(2,13)(3,12)(4,11)(5,10)(6,9)(7,8)", "d=(1,14)(2,13)(3,12)(4,11)(5,10)(6,9)(7,8)", "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,c,c,c,c,c,c>(2,14)(3,13)(4,12)(5,11)(6,10)(7,9)", "b=<1,d*b,b,b,b,b,b,b,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1>(2,14)(3,13)(4,12)(5,11)(6,10)(7,9)", "c=(1,14)(2,13)(3,12)(4,11)(5,10)(6,9)(7,8)", "d=(1,14)(2,13)(3,12)(4,11)(5,10)(6,9)(7,8)", "a*b*c*d"); When the translation term of the affine map is lambda2: NewSphereMachine( "a=(1,14)(2,13)(3,12)(4,11)(5,10)(6,9)(7,8)", "b=(1,14)(2,13)(3,12)(4,11)(5,10)(6,9)(7,8)", "c=(1,13)(2,12)(3,11)(4,10)(5,9)(6,8)", "d=(1,13)(2,12)(3,11)(4,10)(5,9)(6,8)", "a*b*c*d"); When the translation term of the affine map is lambda1+lambda2: NewSphereMachine( "a=(1,14)(2,13)(3,12)(4,11)(5,10)(6,9)(7,8)", "b=(1,14)(2,13)(3,12)(4,11)(5,10)(6,9)(7,8)", "c=<1,d*b,b,b,b,b,b,b,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1>(2,14)(3,13)(4,12)(5,11)(6,10)(7,9)", "d=<1,a^-1*b,b*c*b,b*c*b,b*c*b,b*c*b,b*c*b,b^-1*c*b,b^-1*d*a,b^-1*d*a,b^-1*d*a,b^-1*d*a,b^-1*d*a,b^-1*a>(2,14)(3,13)(4,12)(5,11)(6,10)(7,9)", "a*b*c*d");