These Thurston maps are NET maps for every choice of translation term. They are primitive and have degree 21. 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, 0/3, 0/7, 0/21, 1/21, 1/7, 1/3, 2/3, 1/1, 4/3, 2/1, 3/1, 4/1, 5/1, 6/1 8/1, 9/1, 11/1, 13/1, 15/1, 16/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-infinity,-0.085368) (-0.079741,-0.074298) (-0.068773,-0.064686) (-0.060457,-0.058078) (-0.053243,-0.052034) (-0.048119,-0.047129) (-0.043895,-0.043070) (-0.040352,-0.039654) (-0.037339,-0.036740) (-0.034744,-0.034225) (-0.032487,-0.032033) (-0.030505,-0.030104) (-0.028751,-0.028394) (-0.027187,-0.026869) (-0.025785,-0.025498) (-0.024521,-0.024261) (-0.023374,-0.023138) (-0.022331,-0.022115) (-0.021376,-0.021178) (-0.020499,-0.020318) ( 0.020318,0.020499 ) ( 0.021178,0.021376 ) ( 0.022115,0.022331 ) ( 0.023138,0.023374 ) ( 0.024261,0.024521 ) ( 0.025498,0.025785 ) ( 0.026869,0.027187 ) ( 0.028394,0.028751 ) ( 0.030104,0.030505 ) ( 0.032033,0.032487 ) ( 0.034225,0.034744 ) ( 0.036740,0.037339 ) ( 0.039654,0.040352 ) ( 0.043070,0.043895 ) ( 0.047129,0.048119 ) ( 0.052034,0.053243 ) ( 0.058078,0.060457 ) ( 0.064686,0.068773 ) ( 0.074298,0.079741 ) ( 0.082392,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 (-0.098448,-0.070736) -4/47 EXTENDED HST -> HST (-0.083406,-0.083261) -1/12 EXTENDED HST (-0.073375,-0.063463) -2/29 EXTENDED HST -> HST (-0.073729,-0.052679) -5/79 HST (-0.062541,-0.062459) -1/16 EXTENDED HST (-0.052063,-0.051389) -3/58 HST (-0.053063,-0.049701) -13/253 HST (-0.051306,-0.051258) -2/39 EXTENDED HST (-0.050026,-0.049974) -1/20 EXTENDED HST (-0.052228,-0.044781) -2/41 EXTENDED HST -> HST (-0.047650,-0.040779) -2/45 EXTENDED HST -> HST (-0.042034,-0.039465) -13/319 HST (-0.040749,-0.040335) -3/74 HST (-0.042880,-0.035872) -5/127 HST (-0.039230,-0.039202) -2/51 EXTENDED HST (-0.038477,-0.038446) -1/26 EXTENDED HST (-0.038537,-0.033105) -9/251 HST (-0.035728,-0.035701) -1/28 EXTENDED HST (-0.035281,-0.030041) -2/61 HST (-0.030114,-0.029887) -3/100 HST (-0.030873,-0.028896) -13/435 HST (-0.029859,-0.029843) -2/67 EXTENDED HST (-0.029421,-0.029403) -1/34 EXTENDED HST (-0.028951,-0.028742) -3/104 HST (-0.028403,-0.028201) -3/106 HST (-0.029132,-0.027266) -13/461 HST (-0.028176,-0.028162) -2/71 EXTENDED HST (-0.027786,-0.027770) -1/36 EXTENDED HST (-0.027367,-0.027179) -4/147 HST (-0.026876,-0.026696) -3/112 HST (-0.027578,-0.025809) -13/487 HST (-0.026673,-0.026660) -2/75 EXTENDED HST (-0.026323,-0.026309) -1/38 EXTENDED HST (-0.025947,-0.025778) -4/155 HST (-0.025505,-0.025343) -3/118 HST (-0.026181,-0.024501) -13/513 HST (-0.025322,-0.025311) -2/79 EXTENDED HST (-0.025006,-0.024994) -1/40 EXTENDED HST (-0.024268,-0.024120) -3/124 HST (-0.024918,-0.023318) -13/539 HST (-0.024102,-0.024091) -2/83 EXTENDED HST (-0.023815,-0.023804) -1/42 EXTENDED HST (-0.023144,-0.023010) -3/130 HST (-0.023772,-0.022245) -13/565 HST (-0.022993,-0.022984) -2/87 EXTENDED HST (-0.022733,-0.022722) -1/44 EXTENDED HST (-0.022120,-0.021998) -3/136 HST (-0.022727,-0.021266) -13/591 HST (-0.021982,-0.021974) -2/91 EXTENDED HST (-0.021744,-0.021734) -1/46 EXTENDED HST (-0.021183,-0.021071) -3/142 HST (-0.021769,-0.020370) -13/617 HST (-0.021057,-0.021049) -2/95 EXTENDED HST (-0.020838,-0.020829) -1/48 EXTENDED HST (-0.154333,0.223386 ) 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 because every loop multiplier of the mod 2 slope correspondence graph is at least 1 and the map is rational. 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=(2,21)(3,20)(4,19)(5,18)(6,17)(7,16)(8,15)(9,14)(10,13)(11,12)", "b=(1,21)(2,20)(3,19)(4,18)(5,17)(6,16)(7,15)(8,14)(9,13)(10,12)", "c=(1,21)(2,20)(3,19)(4,18)(5,17)(6,16)(7,15)(8,14)(9,13)(10,12)", "d=<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>(2,21)(3,20)(4,19)(5,18)(6,17)(7,16)(8,15)(9,14)(10,13)(11,12)", "a*b*c*d"); When the translation term of the affine map is lambda1: NewSphereMachine( "a=(1,2)(3,21)(4,20)(5,19)(6,18)(7,17)(8,16)(9,15)(10,14)(11,13)", "b=(2,21)(3,20)(4,19)(5,18)(6,17)(7,16)(8,15)(9,14)(10,13)(11,12)", "c=<1,c^-1,c^-1,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,c,c,c,c,c>(2,21)(3,20)(4,19)(5,18)(6,17)(7,16)(8,15)(9,14)(10,13)(11,12)", "d=<1,d,c^-1,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,c,c,c,c>(1,2)(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 lambda2: NewSphereMachine( "a=(1,20)(2,19)(3,18)(4,17)(5,16)(6,15)(7,14)(8,13)(9,12)(10,11)", "b=(1,21)(2,20)(3,19)(4,18)(5,17)(6,16)(7,15)(8,14)(9,13)(10,12)", "c=(1,21)(2,20)(3,19)(4,18)(5,17)(6,16)(7,15)(8,14)(9,13)(10,12)", "d=(1,20)(2,19)(3,18)(4,17)(5,16)(6,15)(7,14)(8,13)(9,12)(10,11)", "a*b*c*d"); When the translation term of the affine map is lambda1+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,c^-1,c^-1,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,c,c,c,c,c>(2,21)(3,20)(4,19)(5,18)(6,17)(7,16)(8,15)(9,14)(10,13)(11,12)", "c=(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");