These Thurston maps are NET maps for every choice of translation term. They are primitive and have degree 24. 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 14. ALL THURSTON MULTIPLIERS c/d IN UNREDUCED FORM 0/12, 0/24, 2/8, 1/3, 2/6, 2/4, 2/3, 2/2, 3/3, 4/3, 5/3, 2/1, 4/2, 4/1, 10/1 14/1, 21/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-infinity,0.044615) ( 0.046296,0.046875) ( 0.049180,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 (0.044025,0.044983) 3/67 HST (0.044872,0.045000) 13/289 HST (0.044992,0.045087) 5/111 HST (0.044917,0.045208) 6/133 HST (0.045043,0.045369) 9/199 HST (0.045276,0.045455) 25/551 HST (0.045427,0.045438) 95/2091 HST (0.045433,0.045476) 1/22 EXTENDED HST (0.045472,0.045483) 90/1979 HST (0.045478,0.045536) 40/879 HST (0.045507,0.045537) 30/659 HST (0.045524,0.045528) 29/637 HST (0.045528,0.045574) 21/461 HST (0.045556,0.045619) 16/351 HST (0.045586,0.045601) 15/329 HST (0.045597,0.045608) 14/307 HST (0.045604,0.045858) 6/131 HST (0.045819,0.045941) 5/109 HST (0.045936,0.046154) 4/87 HST (0.046040,0.046324) 3/65 HST (0.046716,0.047382) 3/64 HST (0.047325,0.047500) 10/211 HST (0.047493,0.047761) 1/21 EXTENDED HST (0.047727,0.047980) 11/230 HST (0.047826,0.049020) 3/62 HST (0.048408,0.051012) 3/61 HST The supplemental half-space computation shows that these NET maps are rational. SLOPE FUNCTION INFORMATION There are no slope function fixed points p/q with |p| <= 50 and |q| <= 50. The fixed point finder is unable to determine whether there are any slope function fixed points. Number of excluded intervals computed by the fixed point finder: 9907 Here is their union. There are no slope function fixed points whose negative reciprocals lie in any of the following intervals. EXCLUDED INTERVALS FOR THE FIXED POINT COMPUTATION (-infinity,0.046281) ( 0.046281,0.046764) ( 0.046764,infinity) 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 |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,b,b,b,b,b,b,b,b,b,b,b,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1*d^-1>(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,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>(2,24)(3,23)(4,22)(5,21)(6,20)(7,19)(8,18)(9,17)(10,16)(11,15)(12,14)", "d=(1,2)(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 lambda1: 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=(1,23)(2,22)(3,21)(4,20)(5,19)(6,18)(7,17)(8,16)(9,15)(10,14)(11,13)", "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,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>(2,24)(3,23)(4,22)(5,21)(6,20)(7,19)(8,18)(9,17)(10,16)(11,15)(12,14)", "a*b*c*d"); When the translation term of the affine map is 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,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>(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)", "a*b*c*d"); When the translation term of the affine map is lambda1+lambda2: NewSphereMachine( "a=(1,23)(2,22)(3,21)(4,20)(5,19)(6,18)(7,17)(8,16)(9,15)(10,14)(11,13)", "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=(1,23)(2,22)(3,21)(4,20)(5,19)(6,18)(7,17)(8,16)(9,15)(10,14)(11,13)", "d=(1,22)(2,21)(3,20)(4,19)(5,18)(6,17)(7,16)(8,15)(9,14)(10,13)(11,12)(23,24)", "a*b*c*d"); ****************************INTEGER OVERFLOW REPORT***************************** Imminent integer overflow occurred during the computation of a fixed point excluded interval about 1898/41307. Imminent integer overflow halted evaluation of the slope function at slope -8055405/372811 during the search for all slope function fixed points. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 20987/453288. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 2822/60951. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 54547/1178134. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 54547/1178134. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 54547/1178134. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 25947/554846. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 25947/554846. Imminent integer overflow halted evaluation of the slope function at slope -4685131/219097 during the search for all slope function fixed points. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 51313/1097268.