These Thurston maps are NET maps for every choice of translation term. They have degree 16. They are imprimitive, each factoring as a NET map with degree 8 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 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 1/16, 2/8, 2/4, 2/2, 2/1, 4/1 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 INFORMATION There are no slope function fixed points. Number of excluded intervals computed by the fixed point finder: 177 NONTRIVIAL CYCLES 0/1 -> 2/1 -> -2/1 -> 0/1 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 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,b^-1,b,b^-1,b,b^-1,b,b^-1,b,b^-1,b,b>(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)", "b=<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)", "c=<1,1,d,1,c,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)", "d=<1,a,1,d*a,a^-1,b^-1,b*c,b^-1,b,b^-1,b,b^-1,b,b^-1,b,b>(1,3)(2,5)(4,7)(6,9)(8,11)(10,13)(12,15)(14,16)", "a*b*c*d"); When the translation term of the affine map is lambda1: NewSphereMachine( "a=<1,1,d*a,b*c,b^-1,b,b^-1,b,b^-1,b,b^-1,b,b^-1,b,b^-1,b>(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)", "b=<1,a,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)", "c=<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)", "d=(1,4)(3,6)(5,8)(7,10)(9,12)(11,14)(13,16)", "a*b*c*d"); When the translation term of the affine map is lambda2: NewSphereMachine( "a=<1,1,d*a,b*c,b^-1,b,b^-1,b,b^-1,b,b^-1,b,b^-1,b,b^-1,b>(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)", "b=<1,1,d,1,c,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)", "c=<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)", "d=(1,4)(3,6)(5,8)(7,10)(9,12)(11,14)(13,16)", "a*b*c*d"); When the translation term of the affine map is lambda1+lambda2: NewSphereMachine( "a=<1,d*a,a^-1,b^-1,b*c,b^-1,b,b^-1,b,b^-1,b,b^-1,b,b^-1,b,1>(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)", "b=<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)", "c=<1,a,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)", "d=(1,3)(2,5)(4,7)(6,9)(8,11)(10,13)(12,15)(14,16)", "a*b*c*d");