These Thurston maps are NET maps for every choice of translation term. They have degree 8. They are imprimitive, each factoring as a NET map with degree 4 followed by a Euclidean NET map with degree 2. 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 7. ALL THURSTON MULTIPLIERS c/d IN UNREDUCED FORM 0/1, 0/4, 0/8, 2/2, 4/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-25.000000,0.500000 ) ( 0.500000,1.000000 ) ( 1.000000,23.000000) The half-space computation does not determine rationality. EXCLUDED INTERVALS FOR JUST THE SUPPLEMENTAL HALF-SPACE COMPUTATION INTERVAL COMPUTED FOR HST OR EXTENDED HST ( 0.478261,0.520835) 1/2 EXTENDED HST ( 0.923083,1.090925) 1/1 EXTENDED HST -1.499023)(2.500000 infinity EXTENDED 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,d^-1,d*a,c,c^-1,c,c^-1,1>(2,3)(4,5)(6,7)", "b=(2,3)(4,5)(6,7)", "c=<1,1,1,1,1,1,1,1>(1,2)(3,4)(5,6)(7,8)", "d=(1,2)(3,4)(5,6)(7,8)", "a*b*c*d"); When the translation term of the affine map is lambda1: NewSphereMachine( "a=(2,3)(4,5)(6,7)", "b=<1,a,1,1,1,1,1,1>(2,3)(4,5)(6,7)", "c=<1,1,1,1,1,1,1,1>(1,2)(3,4)(5,6)(7,8)", "d=(1,2)(3,4)(5,6)(7,8)", "a*b*c*d"); When the translation term of the affine map is lambda2: NewSphereMachine( "a=(1,2)(3,4)(5,6)(7,8)", "b=<1,1,1,1,1,1,1,1>(1,2)(3,4)(5,6)(7,8)", "c=(2,3)(4,5)(6,7)", "d=<1,c^-1,b^-1*d^-1,c^-1,c,c^-1,c,1>(2,3)(4,5)(6,7)", "a*b*c*d"); When the translation term of the affine map is lambda1+lambda2: NewSphereMachine( "a=(1,2)(3,4)(5,6)(7,8)", "b=<1,1,1,1,1,1,1,1>(1,2)(3,4)(5,6)(7,8)", "c=<1,a,1,1,1,1,1,1>(2,3)(4,5)(6,7)", "d=(2,3)(4,5)(6,7)", "a*b*c*d");