These Thurston maps are NET maps for every choice of translation term. They have degree 34. They are imprimitive, each factoring as a NET map with degree 17 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 12. ALL THURSTON MULTIPLIERS c/d IN UNREDUCED FORM 0/17, 1/34, 1/2, 2/2, 2/1, 4/2, 5/2, 7/2, 4/1, 8/2, 11/2, 6/1, 14/2, 8/1 10/1 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 CYCLES FOUND There are no slope function fixed points p/q with |p| <= 50 and |q| <= 50. NONTRIVIAL CYCLES 0/1 -> 2/1 -> -2/1 -> 0/1 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. FUNDAMENTAL GROUP WREATH RECURSIONS When the translation term of the affine map is 0: NewSphereMachine( "a=<1,a,1,d*a,b*c,c*b^-1,b*c,c*b^-1,b*c,c*b^-1,b*c,c*b^-1,b*c,c*b^-1,b*c,c*b^-1,b*c,c*b^-1,b*c,c*b^-1,b*c,c*b^-1,b*c,c*b^-1,b*c,c*b^-1,b*c,c*b^-1,b*c,c*b^-1,b*c,c*b^-1,b*c,c*b*c>(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)(32,33)", "b=<1,1,1,1,1,c^2,1,c^2,1,c^2,1,c^2,1,c^2,1,c^2,1,c^2,1,c^2,1,c^2,1,c^2,1,c^2,1,c^2,1,c^2,1,c^2,1,c^2>(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)(33,34)", "c=<1,1,d,1,c^2,1,c^2,1,c^2,1,c^2,1,c^2,1,c^2,1,c^2,1,c^2,1,c^2,1,c^2,1,c^2,1,c^2,1,c^2,1,c^2,1,c^2,1>(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)(32,33)", "d=<1,a,1,d*a,a^-1,c*b^-1,b*c,c*b^-1,b*c,c*b^-1,b*c,c*b^-1,b*c,c*b^-1,b*c,c*b^-1,b*c,c*b^-1,b*c,c*b^-1,b*c,c*b^-1,b*c,c*b^-1,b*c,c*b^-1,b*c,c*b^-1,b*c,c*b^-1,b*c,c*b^-1*c,b*c,c*b*c>(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)(30,33)(32,34)", "a*b*c*d"); When the translation term of the affine map is lambda1: NewSphereMachine( "a=<1,1,d*a,b*c,c*b^-1,b*c,c*b^-1,b*c,c*b^-1,b*c,c*b^-1,b*c,c*b^-1,b*c,c*b^-1,b*c,c*b^-1,b*c,c*b^-1,b*c,c*b^-1,b*c,c*b^-1,b*c,c*b^-1,b*c,c*b^-1,b*c,c*b^-1,b*c,c*b^-1,b*c,c*b^-1,b*c>(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)(33,34)", "b=<1,a,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,b>(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)(32,33)", "c=<1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1>(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)(33,34)", "d=(1,4)(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)(31,34)", "a*b*c*d"); When the translation term of the affine map is lambda2: NewSphereMachine( "a=<1,1,d*a,b*c,c*b^-1,b*c,c*b^-1,b*c,c*b^-1,b*c,c*b^-1,b*c,c*b^-1,b*c,c*b^-1,b*c,c*b^-1,b*c,c*b^-1,b*c,c*b^-1,b*c,c*b^-1,b*c,c*b^-1,b*c,c*b^-1,b*c,c*b^-1,b*c,c*b^-1,b*c,c*b^-1,b*c>(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)(33,34)", "b=<1,1,d,1,c^2,1,c^2,1,c^2,1,c^2,1,c^2,1,c^2,1,c^2,1,c^2,1,c^2,1,c^2,1,c^2,1,c^2,1,c^2,1,c^2,1,c^2,1>(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)(32,33)", "c=<1,1,1,1,1,c^2,1,c^2,1,c^2,1,c^2,1,c^2,1,c^2,1,c^2,1,c^2,1,c^2,1,c^2,1,c^2,1,c^2,1,c^2,1,c^2,1,c^2>(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)(33,34)", "d=(1,4)(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)(31,34)", "a*b*c*d"); When the translation term of the affine map is lambda1+lambda2: NewSphereMachine( "a=<1,d*a,a^-1,c*b^-1,b*c,c*b^-1,b*c,c*b^-1,b*c,c*b^-1,b*c,c*b^-1,b*c,c*b^-1,b*c,c*b^-1,b*c,c*b^-1,b*c,c*b^-1,b*c,c*b^-1,b*c,c*b^-1,b*c,c*b^-1,b*c,c*b^-1,b*c,c*b^-1,b*c,c*b^-1,b*c,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)(32,33)", "b=<1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1>(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)(33,34)", "c=<1,a,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,b>(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)(32,33)", "d=(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)(30,33)(32,34)", "a*b*c*d");