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 7. ALL THURSTON MULTIPLIERS c/d IN UNREDUCED FORM 1/21, 1/7, 1/3, 1/1, 3/3, 5/3, 5/1, 11/1, 13/1, 17/1, 19/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-infinity,0.055246) ( 0.056521,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 (0.055092,0.055355) 10/181 HST (0.055312,0.055411) 16/289 HST (0.055351,0.055462) 22/397 HST (0.055437,0.055485) 33/595 HST (0.055451,0.055515) 44/793 HST (0.055495,0.055603) 1/18 EXTENDED HST (0.055556,0.055882) 10/179 HST (0.055873,0.055889) 19/340 HST (0.055880,0.055897) 65/1163 HST (0.055890,0.055908) 9/161 HST (0.055900,0.055918) 35/626 HST (0.055913,0.055929) 17/304 HST (0.055927,0.055934) 58/1037 HST (0.055931,0.055953) 8/143 HST (0.055942,0.055975) 39/697 HST (0.055955,0.055980) 15/268 HST (0.055966,0.056004) 51/911 HST (0.055983,0.056043) 7/125 HST (0.056032,0.056160) 6/107 HST (0.056136,0.058961) 4/71 HST The supplemental half-space computation shows that these NET maps are rational. SLOPE FUNCTION INFORMATION NUMBER OF FIXED POINTS: 5 EQUATOR? FIXED POINT c d 0 lambda1 lambda2 lambda1+lambda2 -18/1 1 21 Yes Yes No No 0/1 1 21 Yes Yes No No -1448/81 1 21 Yes Yes No No -482/27 1 21 Yes Yes No No -1442/81 1 21 Yes Yes No No NUMBER OF EQUATORS: 5 5 0 0 There are no more slope function fixed points. Number of excluded intervals computed by the fixed point finder: 724 NONTRIVIAL CYCLES -125/7 -> -143/8 -> -125/7 The slope function maps every slope to a slope: no slope maps to the nonslope. The slope function orbit of every slope p/q with |p| <= 50 and |q| <= 50 ends in one of the above cycles. 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,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c,c,c,c,c,c,c,c,c,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,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c,c,c,c,c,c,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 lambda1: NewSphereMachine( "a=(1,21)(2,20)(3,19)(4,18)(5,17)(6,16)(7,15)(8,14)(9,13)(10,12)", "b=(1,20)(2,19)(3,18)(4,17)(5,16)(6,15)(7,14)(8,13)(9,12)(10,11)", "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,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c,c,c,c,c,c,c,c,c,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 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,c^-1,c^-1,c^-1,c^-1,c^-1,c,c,c,c,c,c,c,c,c,c*d>(2,21)(3,20)(4,19)(5,18)(6,17)(7,16)(8,15)(9,14)(10,13)(11,12)", "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=(1,20)(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=(1,20)(2,19)(3,18)(4,17)(5,16)(6,15)(7,14)(8,13)(9,12)(10,11)", "d=(1,19)(2,18)(3,17)(4,16)(5,15)(6,14)(7,13)(8,12)(9,11)(20,21)", "a*b*c*d");