These Thurston maps are NET maps for every choice of translation term. They are primitive and have degree 25. 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 7. ALL THURSTON MULTIPLIERS c/d IN UNREDUCED FORM 1/25, 1/5, 3/5, 1/1, 3/1, 7/1, 9/1, 11/1, 13/1, 17/1, 19/1, 21/1, 23/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-infinity,0.045151) ( 0.045956,infinity) The half-space computation does not determine rationality. EXCLUDED INTERVALS FOR JUST THE SUPPLEMENTAL HALF-SPACE COMPUTATION INTERVAL COMPUTED FOR HST OR EXTENDED HST (0.044811,0.045293) 7/155 HST (0.044118,0.045455) 13/287 HST (0.045434,0.045441) 120/2641 HST (0.045437,0.045471) 1/22 EXTENDED HST (0.045455,0.045635) 12/263 HST (0.045631,0.045638) 23/504 HST (0.045634,0.045640) 34/745 HST (0.045639,0.045646) 11/241 HST (0.045646,0.045646) 65/1424 HST (0.045646,0.045650) 43/942 HST (0.045648,0.045655) 21/460 HST (0.045653,0.045657) 31/679 HST (0.045656,0.045658) 41/898 HST (0.045657,0.045666) 10/219 HST (0.045664,0.045682) 19/416 HST (0.045675,0.045685) 37/810 HST (0.045679,0.045690) 9/197 HST (0.045677,0.045705) 53/1160 HST (0.045690,0.045714) 17/372 HST (0.045703,0.045710) 33/722 HST (0.045706,0.045720) 8/175 HST (0.045717,0.045911) 7/153 HST (0.045792,0.046099) 5/109 HST The supplemental half-space computation shows that these NET maps are rational. SLOPE FUNCTION INFORMATION NUMBER OF FIXED POINTS: 6 EQUATOR? FIXED POINT c d 0 lambda1 lambda2 lambda1+lambda2 -22/1 1 25 Yes Yes No No 0/1 1 25 Yes Yes No No -2650/121 1 25 Yes Yes No No -3174/145 1 25 Yes Yes No No -3172/145 1 25 Yes Yes No No -2642/121 1 25 Yes Yes No No NUMBER OF EQUATORS: 6 6 0 0 There are no more slope function fixed points. Number of excluded intervals computed by the fixed point finder: 805 NONTRIVIAL CYCLES -153/7 -> -219/10 -> -197/9 -> -175/8 -> -153/7 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. FUNDAMENTAL GROUP WREATH RECURSIONS When the translation term of the affine map is 0: NewSphereMachine( "a=(2,25)(3,24)(4,23)(5,22)(6,21)(7,20)(8,19)(9,18)(10,17)(11,16)(12,15)(13,14)", "b=(1,25)(2,24)(3,23)(4,22)(5,21)(6,20)(7,19)(8,18)(9,17)(10,16)(11,15)(12,14)", "c=<1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c,c,c,c,c,c,c,c,c,c,c,c*d>(2,25)(3,24)(4,23)(5,22)(6,21)(7,20)(8,19)(9,18)(10,17)(11,16)(12,15)(13,14)", "d=<1,1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c,c,c,c,c,c,c,c,c,c,c,c>(1,2)(3,25)(4,24)(5,23)(6,22)(7,21)(8,20)(9,19)(10,18)(11,17)(12,16)(13,15)", "a*b*c*d"); When the translation term of the affine map is lambda1: NewSphereMachine( "a=(1,25)(2,24)(3,23)(4,22)(5,21)(6,20)(7,19)(8,18)(9,17)(10,16)(11,15)(12,14)", "b=(1,24)(2,23)(3,22)(4,21)(5,20)(6,19)(7,18)(8,17)(9,16)(10,15)(11,14)(12,13)", "c=(1,25)(2,24)(3,23)(4,22)(5,21)(6,20)(7,19)(8,18)(9,17)(10,16)(11,15)(12,14)", "d=<1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c,c,c,c,c,c,c,c,c,c,c,c*d>(2,25)(3,24)(4,23)(5,22)(6,21)(7,20)(8,19)(9,18)(10,17)(11,16)(12,15)(13,14)", "a*b*c*d"); When the translation term of the affine map is lambda2: NewSphereMachine( "a=(1,25)(2,24)(3,23)(4,22)(5,21)(6,20)(7,19)(8,18)(9,17)(10,16)(11,15)(12,14)", "b=<1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c,c,c,c,c,c,c,c,c,c,c,c*d>(2,25)(3,24)(4,23)(5,22)(6,21)(7,20)(8,19)(9,18)(10,17)(11,16)(12,15)(13,14)", "c=(1,25)(2,24)(3,23)(4,22)(5,21)(6,20)(7,19)(8,18)(9,17)(10,16)(11,15)(12,14)", "d=(1,24)(2,23)(3,22)(4,21)(5,20)(6,19)(7,18)(8,17)(9,16)(10,15)(11,14)(12,13)", "a*b*c*d"); When the translation term of the affine map is lambda1+lambda2: NewSphereMachine( "a=(1,24)(2,23)(3,22)(4,21)(5,20)(6,19)(7,18)(8,17)(9,16)(10,15)(11,14)(12,13)", "b=(1,25)(2,24)(3,23)(4,22)(5,21)(6,20)(7,19)(8,18)(9,17)(10,16)(11,15)(12,14)", "c=(1,24)(2,23)(3,22)(4,21)(5,20)(6,19)(7,18)(8,17)(9,16)(10,15)(11,14)(12,13)", "d=(1,23)(2,22)(3,21)(4,20)(5,19)(6,18)(7,17)(8,16)(9,15)(10,14)(11,13)(24,25)", "a*b*c*d");