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} Since no Thurston multiplier is 1, this modular group Hurwitz class contains only finitely many Thurston equivalence classes. The number of pure modular group Hurwitz classes in this modular group Hurwitz class is 10. ALL THURSTON MULTIPLIERS c/d IN UNREDUCED FORM 0/11, 1/22, 1/11, 1/2, 3/2, 5/2, 7/2, 4/1, 9/2, 8/1, 12/1, 16/1, 20/1, 21/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-infinity,0.049810) ( 0.050485,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 (0.049684,0.049894) 14/281 HST (0.049852,0.049929) 24/481 HST (0.049908,0.049950) 36/721 HST (0.049934,0.049964) 50/1001 HST (0.049962,0.050029) 1/20 EXTENDED HST (0.050000,0.050122) 21/419 HST (0.050121,0.050123) 41/818 HST (0.050123,0.050124) 142/2833 HST (0.050124,0.050126) 20/399 HST (0.050126,0.050128) 99/1975 HST (0.050127,0.050130) 39/778 HST (0.050128,0.050131) 77/1536 HST (0.050131,0.050132) 267/5326 HST (0.050132,0.050132) 19/379 EXTENDED HST (0.050132,0.050133) 341/6802 HST (0.050132,0.050132) 322/6423 HST (0.050132,0.050136) 56/1117 HST (0.050135,0.050136) 37/738 HST (0.050135,0.050138) 55/1097 HST (0.050137,0.050141) 18/359 HST (0.050140,0.050142) 89/1775 HST (0.050141,0.050145) 35/698 HST (0.050143,0.050147) 225/4487 HST (0.050145,0.050146) 69/1376 HST (0.050146,0.050151) 17/339 HST (0.050151,0.050153) 33/658 HST (0.050147,0.050163) 131/2612 HST (0.050153,0.050154) 49/977 EXTENDED HST (0.050155,0.050159) 16/319 HST (0.050157,0.050172) 46/917 HST (0.050167,0.050168) 15/299 EXTENDED HST (0.050172,0.050252) 13/259 HST (0.050207,0.050319) 10/199 HST (0.050262,0.050454) 8/159 HST (0.050317,0.050842) 6/119 HST The supplemental half-space computation shows that these NET maps are rational. SLOPE FUNCTION INFORMATION NUMBER OF FIXED POINTS: 4 EQUATOR? FIXED POINT c d 0 lambda1 lambda2 lambda1+lambda2 -20/1 1 22 Yes Yes No No 0/1 1 22 Yes Yes No No -5046/253 1 22 Yes Yes No No -5042/253 1 22 Yes Yes No No NUMBER OF EQUATORS: 4 4 0 0 There are no more slope function fixed points. Number of excluded intervals computed by the fixed point finder: 1058 NONTRIVIAL CYCLES -339/17 -> -359/18 -> -339/17 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 either one of the above cycles or the nonslope. FUNDAMENTAL GROUP WREATH RECURSIONS When the translation term of the affine map is 0: NewSphereMachine( "a=<1,b,b,b,b,b,b,b,b,b,b,b,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1>(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,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,c>(2,22)(3,21)(4,20)(5,19)(6,18)(7,17)(8,16)(9,15)(10,14)(11,13)", "d=<1,d,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>(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 lambda1: 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=(1,21)(2,20)(3,19)(4,18)(5,17)(6,16)(7,15)(8,14)(9,13)(10,12)", "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,c^-1,c^-1,c^-1,c^-1,c^-1,c,c,c,c,c,c,c,c,c,c,c>(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 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,c^-1,c^-1,c^-1,c^-1,c^-1,c,c,c,c,c,c,c,c,c,c,c>(2,22)(3,21)(4,20)(5,19)(6,18)(7,17)(8,16)(9,15)(10,14)(11,13)", "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=(1,21)(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=(1,21)(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)(21,22)", "a*b*c*d");