These Thurston maps are NET maps for every choice of translation term. They are primitive and have degree 5. 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 12. ALL THURSTON MULTIPLIERS c/d IN UNREDUCED FORM 0/1, 0/5, 1/5, 1/1, 2/1 Every NET map in these pure modular group Hurwitz classes is rational. EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-infinity,-0.011056) ( 0.011056, 0.500000) ( 0.500000, 0.662914) ( 0.670360, infinity) SLOPE FUNCTION CYCLES FOUND NUMBER OF FIXED POINTS FOUND: 2 EQUATOR? FIXED POINTS c d 0 lambda1 lambda2 lambda1+lambda2 -2/1 1 5 Yes Yes No No 0/1 1 5 Yes Yes No No NUMBER OF EQUATORS FOUND: 2 2 0 0 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,b,b^-1,b^-1>(2,5)(3,4)", "b=(1,5)(2,4)", "c=<1,c^-1,1,c,c*d>(2,5)(3,4)", "d=<1,1,c^-1,1,c>(1,2)(3,5)", "a*b*c*d"); When the translation term of the affine map is lambda1: NewSphereMachine( "a=(1,5)(2,4)", "b=(1,4)(2,3)", "c=(1,5)(2,4)", "d=<1,c^-1,1,c,c*d>(2,5)(3,4)", "a*b*c*d"); When the translation term of the affine map is lambda2: NewSphereMachine( "a=(1,5)(2,4)", "b=<1,c^-1,1,c,c*d>(2,5)(3,4)", "c=(1,5)(2,4)", "d=(1,4)(2,3)", "a*b*c*d"); When the translation term of the affine map is lambda1+lambda2: NewSphereMachine( "a=(1,4)(2,3)", "b=(1,5)(2,4)", "c=(1,4)(2,3)", "d=(1,3)(4,5)", "a*b*c*d");