These Thurston maps are NET maps for every choice of translation term. They have degree 32. They are imprimitive, each factoring as a NET map with degree 16 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 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 0/16, 2/8, 2/4, 2/2, 4/2 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-infinity,infinity) The half-space computation determines rationality. The supplemental half-space computation is not needed. These NET maps are rational. SLOPE FUNCTION INFORMATION There are no slope function fixed points. Number of excluded intervals computed by the fixed point finder: 7583 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. 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*b,c^-1,b,c^-1,c^-1*b,c^-1,1,c^-1,1,c^-1,1,c^-1,1,1,1,1,1,1,1,c,1,c,1,c,b^-1*c,c,b^-1,c,b^-1*d^-1,c,1>(2,30)(3,31)(4,28)(5,29)(6,26)(7,27)(8,24)(9,25)(10,22)(11,23)(12,20)(13,21)(14,18)(15,19)", "b=(1,30)(2,28)(3,32)(4,26)(5,31)(6,24)(7,29)(8,22)(9,27)(10,20)(11,25)(12,18)(13,23)(14,16)(15,21)(17,19)", "c=(1,32)(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)", "d=(1,31)(2,32)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)", "a*b*c*d"); When the translation term of the affine map is lambda1: NewSphereMachine( "a=(1,31)(2,32)(3,29)(4,30)(5,27)(6,28)(7,25)(8,26)(9,23)(10,24)(11,21)(12,22)(13,19)(14,20)(15,17)(16,18)", "b=(1,29)(3,27)(4,32)(5,25)(6,30)(7,23)(8,28)(9,21)(10,26)(11,19)(12,24)(13,17)(14,22)(16,20)", "c=<1,1,1,1,1,1,1,1,c,c^-1,c,c^-1,c,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1>(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)", "d=(1,32)(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)", "a*b*c*d"); When the translation term of the affine map is lambda2: NewSphereMachine( "a=(1,3)(2,5)(4,7)(6,9)(8,11)(10,13)(12,15)(14,17)(16,19)(18,21)(20,23)(22,25)(24,27)(26,29)(28,31)(30,32)", "b=(1,32)(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)", "c=(1,30)(2,28)(3,32)(4,26)(5,31)(6,24)(7,29)(8,22)(9,27)(10,20)(11,25)(12,18)(13,23)(14,16)(15,21)(17,19)", "d=(1,28)(2,26)(4,24)(5,32)(6,22)(7,31)(8,20)(9,29)(10,18)(11,27)(12,16)(13,25)(15,23)(17,21)", "a*b*c*d"); When the translation term of the affine map is lambda1+lambda2: NewSphereMachine( "a=(1,4)(2,31)(3,6)(5,8)(7,10)(9,12)(11,14)(13,16)(15,18)(17,20)(19,22)(21,24)(23,26)(25,28)(27,30)(29,32)", "b=<1,1,1,1,1,1,1,1,c,c^-1,c,c^-1,c,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1>(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)", "c=(1,29)(3,27)(4,32)(5,25)(6,30)(7,23)(8,28)(9,21)(10,26)(11,19)(12,24)(13,17)(14,22)(16,20)", "d=(1,27)(2,4)(3,25)(5,23)(6,32)(7,21)(8,30)(9,19)(10,28)(11,17)(12,26)(13,15)(14,24)(16,22)(18,20)(29,31)", "a*b*c*d");