These Thurston maps are NET maps for every choice of translation term. They have degree 36. They are imprimitive, each factoring as a NET map with degree 18 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 0/18, 0/36, 2/12, 2/9, 2/6, 2/4, 2/3, 2/2, 4/4, 2/1, 6/3, 8/2, 10/2, 6/1 10/1, 14/1, 30/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-infinity,0.000000) ( 0.000000,0.493391) ( 0.506338,0.994142) ( 1.005810,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 (-0.011603,0.011089) 0/1 EXTENDED HST ( 0.491058,0.509275) 1/2 EXTENDED HST ( 0.962203,1.040893) 1/1 EXTENDED HST The supplemental half-space computation shows that these NET maps are rational. SLOPE FUNCTION INFORMATION NUMBER OF FIXED POINTS FOUND: 1 EQUATOR? FIXED POINT c d 0 lambda1 lambda2 lambda1+lambda2 -2/1 2 12 No No No No NUMBER OF EQUATORS FOUND: 0 0 0 0 The fixed point finder is unable to determine whether there are any more slope function fixed points. Number of excluded intervals computed by the fixed point finder: 11412 Here is their union. There are no more slope function fixed points whose negative reciprocals lie in any of the following intervals. EXCLUDED INTERVALS FOR THE FIXED POINT COMPUTATION ( -infinity,0.675037) ( 0.675037,0.675037) ( 0.675037,0.675037) ( 0.675037,0.675037) ( 0.675037,0.675037) ( 0.675037,0.675037) ( 0.675038,0.675038) ( 0.675038,0.675038) ( 0.675039,0.675039) ( 0.675041,0.675043) ( 0.675045,0.675045) ( 0.675048,0.675048) ( 0.675052,0.675052) ( 0.675056,0.675059) ( 0.675063,0.675063) ( 0.675070,0.675070) ( 0.675075,0.675083) ( 0.675088,0.675093) ( 0.675105,0.675106) ( 0.675120,0.675133) ( 0.675158,0.675160) ( 0.675208,0.675220) ( 0.675292,0.675357) ( 0.675663,0.675688) ( 0.676277,0.676661) ( 0.677391,0.677448) ( 0.678561,0.678582) ( 0.679688,0.680310) ( 0.681807,0.681829) ( 0.684134,0.684288) ( 0.687063,0.687931) ( 0.692278,0.692338) ( 0.699975,0.700025) ( 0.713147,0.715415) ( 0.749842,0.750156) ( 0.998411,1.001584) (1224.972973,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 either one of the above cycles or the nonslope. 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=(2,36)(3,35)(4,34)(5,33)(6,32)(7,31)(8,30)(9,29)(10,28)(11,27)(12,26)(13,25)(14,24)(15,23)(16,22)(17,21)(18,20)", "b=(1,36)(2,35)(3,34)(4,33)(5,32)(6,31)(7,30)(8,29)(9,28)(10,27)(11,26)(12,25)(13,24)(14,23)(15,22)(16,21)(17,20)(18,19)", "c=<1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c,c,c,c,c,c,c,c,c>(2,36)(3,35)(4,34)(5,33)(6,32)(7,31)(8,30)(9,29)(10,28)(11,27)(12,26)(13,25)(14,24)(15,23)(16,22)(17,21)(18,20)", "d=(1,2)(3,36)(4,35)(5,34)(6,33)(7,32)(8,31)(9,30)(10,29)(11,28)(12,27)(13,26)(14,25)(15,24)(16,23)(17,22)(18,21)(19,20)", "a*b*c*d"); When the translation term of the affine map is lambda1: NewSphereMachine( "a=(1,36)(2,35)(3,34)(4,33)(5,32)(6,31)(7,30)(8,29)(9,28)(10,27)(11,26)(12,25)(13,24)(14,23)(15,22)(16,21)(17,20)(18,19)", "b=(1,35)(2,34)(3,33)(4,32)(5,31)(6,30)(7,29)(8,28)(9,27)(10,26)(11,25)(12,24)(13,23)(14,22)(15,21)(16,20)(17,19)", "c=(1,36)(2,35)(3,34)(4,33)(5,32)(6,31)(7,30)(8,29)(9,28)(10,27)(11,26)(12,25)(13,24)(14,23)(15,22)(16,21)(17,20)(18,19)", "d=<1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c,c,c,c,c,c,c,c,c>(2,36)(3,35)(4,34)(5,33)(6,32)(7,31)(8,30)(9,29)(10,28)(11,27)(12,26)(13,25)(14,24)(15,23)(16,22)(17,21)(18,20)", "a*b*c*d"); When the translation term of the affine map is lambda2: NewSphereMachine( "a=(1,36)(2,35)(3,34)(4,33)(5,32)(6,31)(7,30)(8,29)(9,28)(10,27)(11,26)(12,25)(13,24)(14,23)(15,22)(16,21)(17,20)(18,19)", "b=<1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c,c,c,c,c,c,c,c,c>(2,36)(3,35)(4,34)(5,33)(6,32)(7,31)(8,30)(9,29)(10,28)(11,27)(12,26)(13,25)(14,24)(15,23)(16,22)(17,21)(18,20)", "c=(1,36)(2,35)(3,34)(4,33)(5,32)(6,31)(7,30)(8,29)(9,28)(10,27)(11,26)(12,25)(13,24)(14,23)(15,22)(16,21)(17,20)(18,19)", "d=(1,35)(2,34)(3,33)(4,32)(5,31)(6,30)(7,29)(8,28)(9,27)(10,26)(11,25)(12,24)(13,23)(14,22)(15,21)(16,20)(17,19)", "a*b*c*d"); When the translation term of the affine map is lambda1+lambda2: NewSphereMachine( "a=(1,35)(2,34)(3,33)(4,32)(5,31)(6,30)(7,29)(8,28)(9,27)(10,26)(11,25)(12,24)(13,23)(14,22)(15,21)(16,20)(17,19)", "b=(1,36)(2,35)(3,34)(4,33)(5,32)(6,31)(7,30)(8,29)(9,28)(10,27)(11,26)(12,25)(13,24)(14,23)(15,22)(16,21)(17,20)(18,19)", "c=(1,35)(2,34)(3,33)(4,32)(5,31)(6,30)(7,29)(8,28)(9,27)(10,26)(11,25)(12,24)(13,23)(14,22)(15,21)(16,20)(17,19)", "d=(1,34)(2,33)(3,32)(4,31)(5,30)(6,29)(7,28)(8,27)(9,26)(10,25)(11,24)(12,23)(13,22)(14,21)(15,20)(16,19)(17,18)(35,36)", "a*b*c*d"); ****************************INTEGER OVERFLOW REPORT***************************** Imminent integer overflow occurred during the computation of a fixed point excluded interval about 188932/279913. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 718763/1064852. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 718763/1064852. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 482911/715384. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 482911/715384. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 482911/715384. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 482911/715384. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 482911/715384. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 482911/715384. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 482911/715384. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 482911/715384. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 482911/715384. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 482911/715384. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 482911/715384. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 482911/715384. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 482911/715384. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 482911/715384. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 482911/715384. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 482911/715384. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 482911/715384. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 482911/715384. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 482911/715384. Imminent integer overflow halted evaluation of the slope function at slope -4988335/3367313 while computing a fixed point excluded interval about 482911/715384. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 482911/715384. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 482911/715384. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 482911/715384. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 482911/715384. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 482911/715384. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 482911/715384. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 482911/715384. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 482911/715384. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 482911/715384. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 482911/715384. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 482911/715384. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 482911/715384. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 482911/715384. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 482911/715384. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 482911/715384. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 482911/715384. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 482911/715384. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 482911/715384. Imminent integer overflow halted evaluation of the slope function at slope -7849871/5298957 while computing a fixed point excluded interval about 482911/715384. Imminent integer overflow halted evaluation of the slope function at slope -8048737/5433199 while computing a fixed point excluded interval about 482911/715384. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 482911/715384. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 482911/715384. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 482911/715384. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 482911/715384. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 482911/715384. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 482911/715384. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 482911/715384.