These Thurston maps all have degree 2. There are choices of translation term b for which the resulting Thurston map is not a NET map. The postcritical set has 4 points if b = 0. The postcritical set has 3 points if b = lambda1. The postcritical set has 4 points if b = lambda2. The postcritical set has 3 points if b = lambda1+lambda2. PURE MODULAR GROUP HURWITZ EQUIVALENCE CLASSES FOR TRANSLATIONS {0,lambda2} This pure modular group Hurwitz class contains 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 4. ALL THURSTON MULTIPLIERS c/d IN UNREDUCED FORM 0/1, 1/2, 1/1 Every NET map in this pure modular group Hurwitz class is rational because every loop multiplier in the modulo 2 correspondence graph is less than 1. EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-170.710678,0.000000 ) ( 0.000000,170.710678) SLOPE FUNCTION INFORMATION NUMBER OF FIXED POINTS: 1 EQUATOR? FIXED POINT c d 0 lambda1 lambda2 lambda1+lambda2 1/0 1 2 No * No * NUMBER OF EQUATORS: 0 * 0 * There are no more slope function fixed points. Number of excluded intervals computed by the fixed point finder: 11 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 |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=", "b=<1,c*d*c^-1>", "c=(1,2)", "d=(1,2)", "a*b*c*d"); When the translation term of the affine map is lambda2: NewSphereMachine( "a=<1,c>(1,2)", "b=(1,2)", "c=<1,c*d*c^-1>", "d=", "a*b*c*d");