These Thurston maps are NET maps for every choice of translation term. They are primitive and have degree 17. 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 0/17, 1/17, 1/1, 2/1, 3/1, 4/1, 5/1, 6/1, 7/1, 8/1, 11/1, 14/1, 15/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-infinity,0.066275) ( 0.067903,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 (0.066080,0.066438) 12/181 HST (0.066340,0.066522) 20/301 HST (0.066482,0.066568) 31/466 HST (0.066539,0.066598) 46/691 HST (0.066594,0.066731) 1/15 EXTENDED HST (0.066730,0.066761) 57/854 HST (0.066745,0.066779) 46/689 HST (0.066765,0.066831) 35/524 HST (0.066797,0.066829) 30/449 HST (0.066818,0.066854) 26/389 HST (0.066841,0.066891) 23/344 HST (0.066867,0.066906) 20/299 HST (0.066894,0.066929) 18/269 HST (0.066927,0.066941) 17/254 HST (0.066929,0.066964) 16/239 HST (0.066964,0.066965) 15/224 EXTENDED HST (0.066964,0.066968) 134/2001 HST (0.066967,0.066970) 89/1329 HST (0.066968,0.066974) 44/657 HST (0.066973,0.066974) 189/2822 HST (0.066974,0.066975) 29/433 EXTENDED HST (0.066975,0.066976) 275/4106 HST (0.066975,0.066978) 72/1075 HST (0.066978,0.066981) 43/642 HST (0.066978,0.066990) 14/209 HST (0.066985,0.066997) 55/821 HST (0.066993,0.066994) 41/612 EXTENDED HST (0.066995,0.067003) 27/403 HST (0.066997,0.067010) 53/791 HST (0.067010,0.067011) 13/194 EXTENDED HST (0.067007,0.067021) 77/1149 HST (0.067015,0.067023) 38/567 HST (0.067021,0.067025) 163/2432 HST (0.067024,0.067024) 25/373 EXTENDED HST (0.067025,0.067026) 112/1671 HST (0.067026,0.067029) 62/925 HST (0.067029,0.067029) 37/552 EXTENDED HST (0.067024,0.067041) 49/731 HST (0.067033,0.067049) 12/179 HST (0.067044,0.067055) 35/522 HST (0.067055,0.067056) 23/343 EXTENDED HST (0.067052,0.067060) 103/1536 HST (0.067057,0.067058) 80/1193 HST (0.067059,0.067059) 57/850 EXTENDED HST (0.067060,0.067062) 34/507 HST (0.067062,0.067070) 45/671 HST (0.067068,0.067071) 122/1819 HST (0.067071,0.067075) 11/164 EXTENDED HST (0.067074,0.067200) 9/134 HST (0.067166,0.067369) 7/104 HST (0.067310,0.067693) 6/89 HST (0.067505,0.069293) 4/59 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,d*b,b,b,b,b,b,b,b,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1>(2,17)(3,16)(4,15)(5,14)(6,13)(7,12)(8,11)(9,10)", "b=(1,17)(2,16)(3,15)(4,14)(5,13)(6,12)(7,11)(8,10)", "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>(2,17)(3,16)(4,15)(5,14)(6,13)(7,12)(8,11)(9,10)", "d=(1,2)(3,17)(4,16)(5,15)(6,14)(7,13)(8,12)(9,11)", "a*b*c*d"); When the translation term of the affine map is lambda1: NewSphereMachine( "a=(1,17)(2,16)(3,15)(4,14)(5,13)(6,12)(7,11)(8,10)", "b=(1,16)(2,15)(3,14)(4,13)(5,12)(6,11)(7,10)(8,9)", "c=(1,17)(2,16)(3,15)(4,14)(5,13)(6,12)(7,11)(8,10)", "d=<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>(2,17)(3,16)(4,15)(5,14)(6,13)(7,12)(8,11)(9,10)", "a*b*c*d"); When the translation term of the affine map is lambda2: NewSphereMachine( "a=(1,17)(2,16)(3,15)(4,14)(5,13)(6,12)(7,11)(8,10)", "b=<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>(2,17)(3,16)(4,15)(5,14)(6,13)(7,12)(8,11)(9,10)", "c=(1,17)(2,16)(3,15)(4,14)(5,13)(6,12)(7,11)(8,10)", "d=(1,16)(2,15)(3,14)(4,13)(5,12)(6,11)(7,10)(8,9)", "a*b*c*d"); When the translation term of the affine map is lambda1+lambda2: NewSphereMachine( "a=(1,16)(2,15)(3,14)(4,13)(5,12)(6,11)(7,10)(8,9)", "b=(1,17)(2,16)(3,15)(4,14)(5,13)(6,12)(7,11)(8,10)", "c=(1,16)(2,15)(3,14)(4,13)(5,12)(6,11)(7,10)(8,9)", "d=(1,15)(2,14)(3,13)(4,12)(5,11)(6,10)(7,9)(16,17)", "a*b*c*d");