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 0/3, 0/7, 0/21, 1/21, 1/7, 1/3, 2/3, 1/1, 2/1, 3/1, 4/1, 5/1, 6/1, 9/1, 11/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-infinity,-1.506147) (-1.494954,-1.382848) (-1.382485,-1.379513) (-1.377545,-1.335423) (-1.327316,-1.317778) (-1.316866,-1.304982) (-1.303620,-1.302417) (-1.293940,-1.255207) (-1.244479,-1.209939) (-1.205276,-1.204989) (-1.194795,-1.185879) (-1.184412,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 (-1.525354,-1.478309) -3/2 EXTENDED HST (-1.384364,-1.381020) -112/81 HST (-1.379802,-1.377039) -40/29 EXTENDED HST -> HST (-1.335683,-1.331063) -4/3 EXTENDED HST (-1.332308,-1.322591) -77/58 HST (-1.320091,-1.315136) -112/85 HST (-1.317624,-1.317294) -83/63 HST (-1.317110,-1.317036) -54/41 EXTENDED HST (-1.305295,-1.299659) -30/23 EXTENDED HST -> HST (-1.299670,-1.298488) -152/117 HST (-1.299087,-1.297908) -87/67 HST (-1.298359,-1.297371) -61/47 HST (-1.297388,-1.297206) -48/37 EXTENDED HST (-1.297263,-1.296793) -179/138 HST (-1.297040,-1.296505) -83/64 HST (-1.296814,-1.293411) -35/27 EXTENDED HST -> HST (-1.294242,-1.293993) -22/17 EXTENDED HST (-1.255823,-1.253059) -64/51 HST (-1.253474,-1.252264) -104/83 HST (-1.252728,-1.251771) -139/111 HST (-1.252095,-1.251390) -179/143 HST (-1.251674,-1.251062) -229/183 HST (-1.251290,-1.250808) -299/239 HST (-1.250972,-1.250633) -389/311 HST (-1.250658,-1.249359) -5/4 EXTENDED HST (-1.249474,-1.249169) -466/373 HST (-1.249325,-1.248944) -361/289 HST (-1.249134,-1.248642) -281/225 HST (-1.248874,-1.247464) -176/141 HST (-1.248209,-1.246980) -136/109 HST (-1.247649,-1.244606) -86/69 HST (-1.246198,-1.243464) -61/49 HST (-1.210989,-1.208699) -75/62 HST (-1.209322,-1.209283) -52/43 EXTENDED HST (-1.209401,-1.207982) -139/115 HST (-1.208365,-1.208302) -29/24 EXTENDED HST (-1.208015,-1.206794) -64/53 HST (-1.206972,-1.206822) -35/29 EXTENDED HST (-1.206947,-1.204239) -41/34 EXTENDED HST -> HST (-1.205786,-1.202331) -59/49 HST (-1.203354,-1.196754) -6/5 EXTENDED HST (-1.197963,-1.195219) -67/56 HST (-1.196161,-1.195993) -61/51 HST (-1.195661,-1.195644) -55/46 EXTENDED HST (-1.195220,-1.195210) -1249/1045 HST (-1.195214,-1.195185) -349/292 HST (-1.195188,-1.195167) -496/415 HST (-1.195174,-1.195157) -643/538 HST (-1.195159,-1.195084) -49/41 EXTENDED HST (-1.195272,-1.194618) -141/118 HST (-1.194811,-1.194799) -92/77 EXTENDED HST (-1.186634,-1.185405) -134/113 HST (-1.185728,-1.185403) -83/70 HST (-1.186180,-1.184543) -211/178 HST (-1.185270,-1.183900) -32/27 EXTENDED HST -> 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: 9701 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. 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,1,1,1,1,1,1,1,b^-1,b^-1*c,b^-1*c,b^-1*c,b^-1*c,b^-1*c>(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,a*b,a*b,a*b,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,c,c*d,c*d,c*d,c*d>(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=<1,b,c^-1*b,c^-1*b,c^-1*b,c^-1*b,b,b,1,1,1,1,1,1,1,b^-1,b^-1*c,b^-1*c,b^-1*c,b^-1*c,b^-1*c>(2,21)(3,20)(4,19)(5,18)(6,17)(7,16)(8,15)(9,14)(10,13)(11,12)", "c=<1,a*b,a*b,a*b,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,c,c*d,c*d,c*d,c*d>(2,21)(3,20)(4,19)(5,18)(6,17)(7,16)(8,15)(9,14)(10,13)(11,12)", "d=<1,1,a*b,a*b,a*b,c^-1,1,1,1,1,1,1,1,1,1,1,1,c,c*d,c*d,c*d>(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,a*b,a*b,a*b,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,c,c*d,c*d,c*d,c*d>(2,21)(3,20)(4,19)(5,18)(6,17)(7,16)(8,15)(9,14)(10,13)(11,12)", "c=<1,b,c^-1*b,c^-1*b,c^-1*b,c^-1*b,b,b,1,1,1,1,1,1,1,b^-1,b^-1*c,b^-1*c,b^-1*c,b^-1*c,b^-1*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");