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 only finitely many Thurston equivalence classes. However, this modular group Hurwitz class contains 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, 3/3, 2/1, 3/1, 4/1, 5/1, 6/1, 7/1 12/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-infinity,-1.382848) (-1.381100,-1.377466) (-1.374123,-1.265373) (-1.262306,-1.255207) (-1.243399,-1.243080) (-1.240000,-1.211092) (-1.207659,-1.206272) (-1.195443,-1.194752) (-1.190591,-1.187720) (-1.187215,-1.170006) (-1.164526,-1.160984) (-1.159704,-1.000000) (-1.000000,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 (-1.384364,-1.381020) -47/34 EXTENDED HST -> HST (-1.386026,-1.370686) -73/53 HST (-1.375653,-1.374354) -11/8 EXTENDED HST (-1.270490,-1.260479) -43/34 EXTENDED HST -> HST (-1.264256,-1.260219) -24/19 EXTENDED HST -> HST (-1.256538,-1.252993) -64/51 HST (-1.254396,-1.251671) -109/87 HST (-1.251748,-1.251572) -189/151 HST (-1.251914,-1.251278) -199/159 HST (-1.251721,-1.250786) -249/199 HST (-1.251110,-1.248860) -5/4 EXTENDED HST (-1.249016,-1.247413) -176/141 HST (-1.248215,-1.246210) -111/89 HST (-1.247137,-1.245825) -91/73 HST (-1.246422,-1.246330) -86/69 HST (-1.246309,-1.241359) -51/41 HST (-1.242152,-1.235260) -31/25 EXTENDED HST -> HST (-1.212291,-1.209508) -132/109 HST (-1.210612,-1.210440) -23/19 EXTENDED HST (-1.210112,-1.208459) -52/43 HST (-1.208755,-1.208137) -429/355 HST (-1.208405,-1.208261) -29/24 EXTENDED HST (-1.208738,-1.207447) -238/197 HST (-1.208108,-1.207722) -151/125 HST (-1.207988,-1.207606) -93/77 HST (-1.206308,-1.206067) -117/97 HST (-1.206505,-1.205717) -199/165 HST (-1.206006,-1.204941) -41/34 EXTENDED HST -> HST (-1.205577,-1.203041) -53/44 HST (-1.203084,-1.202507) -83/69 HST (-1.202552,-1.202070) -101/84 HST (-1.202081,-1.201963) -119/99 HST (-1.202074,-1.201680) -125/104 HST (-1.201748,-1.201413) -149/124 HST (-1.201510,-1.201220) -173/144 HST (-1.201329,-1.201073) -197/164 HST (-1.201156,-1.200933) -227/189 HST (-1.201165,-1.200641) -263/219 HST (-1.200700,-1.200564) -377/314 HST (-1.200635,-1.199369) -6/5 EXTENDED HST (-1.199381,-1.199233) -349/291 HST (-1.199312,-1.199140) -313/261 HST (-1.199222,-1.199027) -277/231 HST (-1.199128,-1.198426) -199/166 HST (-1.198795,-1.198513) -181/151 HST (-1.198670,-1.198333) -163/136 HST (-1.198474,-1.197252) -115/96 HST (-1.197877,-1.197329) -103/86 HST (-1.197556,-1.195616) -73/61 HST (-1.196697,-1.195820) -67/56 HST (-1.196359,-1.195385) -61/51 HST (-1.195945,-1.194849) -55/46 HST (-1.195353,-1.194148) -865/724 HST (-1.194750,-1.193291) -43/36 EXTENDED HST -> HST (-1.193871,-1.189166) -31/26 EXTENDED HST -> HST (-1.187940,-1.187440) -348/293 HST (-1.187662,-1.187337) -19/16 EXTENDED HST (-1.187428,-1.187245) -1819/1532 HST (-1.187336,-1.187131) -279/235 HST (-1.170520,-1.162418) -7/6 EXTENDED HST (-1.163621,-1.153801) -29/25 EXTENDED HST -> HST (-1.010180,-0.988666) -1/1 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. 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^-1,1,1,1,1,1,1,1,1,1,1,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^-1,1,1,1,1,1,1,1,1,1,1,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^-1,1,1,1,1,1,1,1,1,1,1,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");