These Thurston maps are NET maps for every choice of translation term. They have degree 18. They are imprimitive, each factoring as a NET map with degree 3 followed by a Euclidean NET map with degree 6. PURE MODULAR GROUP HURWITZ EQUIVALENCE CLASSES FOR TRANSLATIONS {0,lambda1} {lambda2,lambda1+lambda2} Since no Thurston multiplier is 1, this modular group Hurwitz class contains only finitely many Thurston equivalence classes. The number of pure modular group Hurwitz classes in this modular group Hurwitz class is 3. ALL THURSTON MULTIPLIERS c/d IN UNREDUCED FORM 1/6, 3/6, 2/3, 6/3 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-161.237244,-0.011544 ) ( 0.011544,161.237244) The half-space computation does not determine rationality. EXCLUDED INTERVALS FOR JUST THE SUPPLEMENTAL HALF-SPACE COMPUTATION INTERVAL COMPUTED FOR HST OR EXTENDED HST (-0.061167,0.057648) 0/1 EXTENDED HST -9.347656)(9.348633 infinity EXTENDED HST The supplemental half-space computation shows that these NET maps are rational. SLOPE FUNCTION INFORMATION NUMBER OF FIXED POINTS: 4 EQUATOR? FIXED POINT c d 0 lambda1 lambda2 lambda1+lambda2 2/1 1 6 No No No No 1/0 2 3 No No No No -2/1 1 6 No No No No 0/1 3 6 No No No No NUMBER OF EQUATORS: 0 0 0 0 There are no more slope function fixed points. Number of excluded intervals computed by the fixed point finder: 2577 There are no equators because both elementary divisors are greater than 1. No nontrivial cycles were found. The slope function maps every slope to a slope: no slope maps to the nonslope. The slope function orbit of every slope p/q with |p| <= 50 and |q| <= 50 ends in one of the above cycles. 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=<1,1,a*b,a*b,1,1,b,1,1,1,1,1,1,1,1,b^-1,c*d,1>(2,6)(3,17)(4,16)(5,9)(7,13)(8,12)(11,15)(14,18)", "b=(1,16)(2,3)(4,13)(5,6)(7,10)(8,9)(11,12)(14,15)(17,18)", "c=<1,1,a*b,1,1,c^-1,1,1,1,1,1,1,1,1,c,1,1,c*d>(1,2)(3,18)(4,5)(6,15)(7,8)(9,12)(10,11)(13,14)(16,17)", "d=(1,17)(2,4)(5,7)(6,18)(8,10)(9,15)(11,13)(14,16)", "a*b*c*d"); When the translation term of the affine map is lambda1: NewSphereMachine( "a=<1,1,a*b,1,1,1,b,1,1,1,1,1,1,1,1,b^-1,c*d,1>(1,4)(2,6)(3,17)(5,9)(7,16)(8,12)(10,13)(11,15)(14,18)", "b=<1,1,1,a*b,1,1,b,1,1,1,1,1,1,1,1,b^-1,1,1>(2,3)(4,16)(5,6)(7,13)(8,9)(11,12)(14,15)(17,18)", "c=<1,1,1,1,1,c^-1,1,1,1,1,1,1,1,1,c,1,1,c*d>(1,2)(4,5)(6,18)(7,8)(9,15)(10,11)(13,14)(16,17)", "d=(1,17)(2,4)(3,6)(5,7)(8,10)(9,18)(11,13)(12,15)(14,16)", "a*b*c*d"); When the translation term of the affine map is lambda2: NewSphereMachine( "a=<1,a*b,c^-1,1,1,1,1,1,1,1,1,c,1,1,c*d,c*d,1,1>(1,5)(2,16)(3,15)(4,8)(6,12)(7,11)(10,14)(13,17)", "b=<1,1,a*b,1,1,c^-1,1,1,1,1,1,1,1,1,c,1,1,c*d>(1,2)(3,18)(4,5)(6,15)(7,8)(9,12)(10,11)(13,14)(16,17)", "c=(1,16)(2,3)(4,13)(5,6)(7,10)(8,9)(11,12)(14,15)(17,18)", "d=(1,13)(2,18)(3,5)(4,10)(6,8)(9,11)(12,14)(15,17)", "a*b*c*d"); When the translation term of the affine map is lambda1+lambda2: NewSphereMachine( "a=<1,a*b,a*b,1,1,c^-1,1,1,1,1,1,1,1,1,c,c*d,1,c*d>(1,5)(2,16)(3,18)(4,8)(6,15)(7,11)(9,12)(10,14)(13,17)", "b=<1,1,1,1,1,c^-1,1,1,1,1,1,1,1,1,c,1,1,c*d>(1,2)(4,5)(6,18)(7,8)(9,15)(10,11)(13,14)(16,17)", "c=<1,1,1,a*b,1,1,b,1,1,1,1,1,1,1,1,b^-1,1,1>(2,3)(4,16)(5,6)(7,13)(8,9)(11,12)(14,15)(17,18)", "d=(1,16)(2,18)(3,5)(4,13)(6,8)(7,10)(9,11)(12,14)(15,17)", "a*b*c*d");