These Thurston maps are NET maps for every choice of translation term. They are primitive and have degree 22. 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 24. ALL THURSTON MULTIPLIERS c/d IN UNREDUCED FORM 0/1, 0/11, 0/22, 1/22, 1/11, 1/2, 1/1, 2/2, 3/2, 2/1, 4/2, 5/2, 3/1, 7/2 5/1, 6/1, 7/1, 9/1, 10/1, 13/1, 18/1, 19/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-infinity,-0.108540) (-0.106961,-0.102693) (-0.102487,-0.101599) (-0.097444,-0.093890) (-0.092706,-0.089181) (-0.088112,-0.085195) (-0.081551,-0.079047) (-0.078206,-0.075682) (-0.074911,-0.072792) (-0.070115,-0.068256) (-0.067628,-0.065732) (-0.065150,-0.063542) (-0.061492,-0.060057) (-0.059571,-0.058095) (-0.057639,-0.056655) (-0.054498,-0.053617) (-0.053229,-0.052048) (-0.051682,-0.050889) (-0.049142,-0.048424) (-0.048107,-0.047140) (-0.046840,-0.046188) (-0.044744,-0.044149) (-0.043885,-0.043079) (-0.042828,-0.042282) (-0.041069,-0.040567) (-0.040344,-0.039662) (-0.037332,-0.036747) (-0.034738,-0.034231) (-0.032481,-0.032038) (-0.030500,-0.030109) (-0.028747,-0.028398) (-0.027184,-0.026872) (-0.025782,-0.025502) (-0.024518,-0.024264) (-0.023372,-0.023141) (-0.022328,-0.022117) (-0.021374,-0.021181) (-0.020497,-0.020320) ( 0.020320,0.020497 ) ( 0.021181,0.021374 ) ( 0.022117,0.022328 ) ( 0.023141,0.023372 ) ( 0.024264,0.024518 ) ( 0.025502,0.025782 ) ( 0.026872,0.027184 ) ( 0.028398,0.028747 ) ( 0.030109,0.030500 ) ( 0.032038,0.032481 ) ( 0.034231,0.034738 ) ( 0.036747,0.037332 ) ( 0.039662,0.040344 ) ( 0.040567,0.041069 ) ( 0.042282,0.042828 ) ( 0.043079,0.043885 ) ( 0.044149,0.044744 ) ( 0.046188,0.046840 ) ( 0.047140,0.048107 ) ( 0.048424,0.049142 ) ( 0.050889,0.051682 ) ( 0.052048,0.053229 ) ( 0.053617,0.054498 ) ( 0.056655,0.057639 ) ( 0.058095,0.059571 ) ( 0.060057,0.061492 ) ( 0.063542,0.065150 ) ( 0.065732,0.067628 ) ( 0.068256,0.070115 ) ( 0.072792,0.074911 ) ( 0.075682,0.078206 ) ( 0.079047,0.081551 ) ( 0.085195,0.088112 ) ( 0.089181,0.092706 ) ( 0.093890,0.097444 ) ( 0.101599,0.102487 ) ( 0.102693,0.106961 ) ( 0.108540,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 (-0.113879,-0.101465) -4/37 EXTENDED HST -> HST (-0.107195,-0.107090) -3/28 EXTENDED HST (-0.112763,-0.089923) -7/69 HST (-0.100137,-0.099863) -1/10 EXTENDED HST (-0.093752,-0.083435) -4/45 EXTENDED HST -> HST (-0.088271,-0.088200) -3/34 EXTENDED HST (-0.084828,-0.082035) -69/827 HST (-0.083429,-0.083238) -1/12 EXTENDED HST (-0.082255,-0.081682) -5/61 HST (-0.081716,-0.081639) -37/453 HST (-0.081665,-0.081600) -4/49 EXTENDED HST (-0.081620,-0.081471) -23/282 HST (-0.084343,-0.073662) -23/291 HST (-0.078976,-0.078919) -3/38 EXTENDED HST (-0.079267,-0.065261) -4/55 HST (-0.071499,-0.071359) -1/14 EXTENDED HST (-0.066378,-0.064139) -34/521 HST (-0.065237,-0.065198) -3/46 EXTENDED HST (-0.069286,-0.056991) -4/63 HST (-0.062554,-0.062447) -1/16 EXTENDED HST (-0.056832,-0.056377) -3/53 HST (-0.061537,-0.050582) -4/71 HST (-0.055598,-0.055513) -1/18 EXTENDED HST (-0.050614,-0.050397) -5/99 HST (-0.056236,-0.044429) -7/139 HST (-0.050034,-0.049966) -1/20 EXTENDED HST (-0.047246,-0.041023) -23/521 HST (-0.044127,-0.044109) -3/68 EXTENDED HST (-0.043426,-0.037684) -23/567 HST (-0.040548,-0.040533) -3/74 EXTENDED HST (-0.039336,-0.035969) -9/239 HST (-0.037654,-0.037534) -5/133 HST (-0.037506,-0.037494) -3/80 EXTENDED HST (-0.039468,-0.032376) -6/167 HST (-0.035732,-0.035697) -1/28 EXTENDED HST (-0.033878,-0.030046) -4/125 HST (-0.031920,-0.031910) -3/94 EXTENDED HST (-0.031899,-0.031595) -2/63 HST (-0.031263,-0.031237) -1/32 EXTENDED HST (-0.031844,-0.028239) -7/233 HST (-0.030004,-0.029996) -3/100 EXTENDED HST (-0.029986,-0.029717) -2/67 HST (-0.029424,-0.029400) -1/34 EXTENDED HST (-0.028289,-0.028050) -2/71 HST (-0.028093,-0.027982) -3/107 HST (-0.030669,-0.025137) -4/143 HST (-0.027788,-0.027767) -1/36 EXTENDED HST (-0.025153,-0.025099) -5/199 HST (-0.028082,-0.022084) -7/279 HST (-0.025009,-0.024991) -1/40 EXTENDED HST (-0.023411,-0.020751) -7/317 HST (-0.022061,-0.022057) -3/136 EXTENDED HST (-0.022051,-0.021905) -2/91 HST (-0.021746,-0.021733) -1/46 EXTENDED HST (-0.020765,-0.020729) -5/241 HST (-0.020731,-0.020726) -37/1785 HST (-0.020727,-0.020723) -4/193 EXTENDED HST (-0.020725,-0.020715) -23/1110 HST (-0.020720,-0.020659) -3/145 HST (-0.020683,-0.020555) -2/97 HST (-0.022040,-0.019063) -23/1119 HST (-0.020550,-0.020546) -3/146 EXTENDED HST (-0.111608,0.134102 ) 0/1 EXTENDED HST The supplemental half-space computation shows that 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: 2758 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,b,c^-1*b,c^-1*b,c^-1*b,c^-1*b,b,b,b,b,b,b,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1*c,b^-1*c,b^-1*c,b^-1*c,b^-1*c>(2,22)(3,21)(4,20)(5,19)(6,18)(7,17)(8,16)(9,15)(10,14)(11,13)", "b=(1,22)(2,21)(3,20)(4,19)(5,18)(6,17)(7,16)(8,15)(9,14)(10,13)(11,12)", "c=(1,22)(2,21)(3,20)(4,19)(5,18)(6,17)(7,16)(8,15)(9,14)(10,13)(11,12)", "d=<1,c^-1,c^-1,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,c,c,c,c,c*d>(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: NewSphereMachine( "a=(1,2)(3,22)(4,21)(5,20)(6,19)(7,18)(8,17)(9,16)(10,15)(11,14)(12,13)", "b=<1,b,c^-1*b,c^-1*b,c^-1*b,c^-1*b,b,b,b,b,b,b,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1*c,b^-1*c,b^-1*c,b^-1*c,b^-1*c>(2,22)(3,21)(4,20)(5,19)(6,18)(7,17)(8,16)(9,15)(10,14)(11,13)", "c=<1,c^-1,c^-1,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,c,c,c,c,c*d>(2,22)(3,21)(4,20)(5,19)(6,18)(7,17)(8,16)(9,15)(10,14)(11,13)", "d=<1,1,c^-1,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,c,c,c,c>(1,2)(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 lambda2: NewSphereMachine( "a=(1,21)(2,20)(3,19)(4,18)(5,17)(6,16)(7,15)(8,14)(9,13)(10,12)", "b=(1,22)(2,21)(3,20)(4,19)(5,18)(6,17)(7,16)(8,15)(9,14)(10,13)(11,12)", "c=(1,22)(2,21)(3,20)(4,19)(5,18)(6,17)(7,16)(8,15)(9,14)(10,13)(11,12)", "d=(1,21)(2,20)(3,19)(4,18)(5,17)(6,16)(7,15)(8,14)(9,13)(10,12)", "a*b*c*d"); When the translation term of the affine map is lambda1+lambda2: NewSphereMachine( "a=(1,22)(2,21)(3,20)(4,19)(5,18)(6,17)(7,16)(8,15)(9,14)(10,13)(11,12)", "b=<1,c^-1,c^-1,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,c,c,c,c,c*d>(2,22)(3,21)(4,20)(5,19)(6,18)(7,17)(8,16)(9,15)(10,14)(11,13)", "c=<1,b,c^-1*b,c^-1*b,c^-1*b,c^-1*b,b,b,b,b,b,b,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1*c,b^-1*c,b^-1*c,b^-1*c,b^-1*c>(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)", "a*b*c*d");