These Thurston maps are NET maps for every choice of translation term. They are primitive and have degree 26. 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 0/13, 0/26, 1/26, 1/13, 1/2, 1/1, 2/2, 3/2, 2/1, 5/2, 3/1, 7/2, 4/1, 5/1 6/1, 7/1, 8/1, 9/1, 11/1, 14/1, 15/1, 16/1, 17/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-infinity,-1.170429) (-1.162301,-1.162014) (-1.161564,-1.159248) (-1.155508,-1.152955) (-1.148936,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 (-1.172053,-1.168656) -55/47 HST (-1.168737,-1.168376) -104/89 HST (-1.169078,-1.167293) -118/101 HST (-1.167587,-1.167036) -314/269 HST (-1.167281,-1.166094) -7/6 EXTENDED HST (-1.166522,-1.165511) -302/259 HST (-1.166015,-1.165203) -183/157 HST (-1.165575,-1.165551) -176/151 HST (-1.165547,-1.163748) -106/91 HST (-1.164749,-1.163128) -78/67 HST (-1.164002,-1.162798) -57/49 HST (-1.162832,-1.162751) -50/43 EXTENDED HST (-1.163462,-1.161972) -143/123 HST (-1.162503,-1.162497) -93/80 EXTENDED HST (-1.162222,-1.161780) -165/142 HST (-1.161825,-1.161733) -1228/1057 HST (-1.161769,-1.161760) -79/68 EXTENDED HST (-1.162022,-1.161406) -194/167 HST (-1.161675,-1.161555) -115/99 HST (-1.159364,-1.158441) -51/44 HST (-1.159271,-1.157794) -117/101 HST (-1.158022,-1.157771) -22/19 EXTENDED HST (-1.158675,-1.154885) -37/32 EXTENDED HST -> HST (-1.153191,-1.152504) -98/85 HST (-1.152806,-1.152324) -68/59 HST (-1.152331,-1.152240) -174/151 HST (-1.152296,-1.152164) -386/335 HST (-1.152184,-1.152164) -53/46 EXTENDED HST (-1.152202,-1.152083) -886/769 HST (-1.152144,-1.152107) -462/401 HST (-1.152114,-1.152111) -409/355 HST (-1.152106,-1.152101) -356/309 HST (-1.152102,-1.151642) -91/79 HST (-1.151648,-1.151602) -281/244 HST (-1.151605,-1.151574) -433/376 HST (-1.151583,-1.151560) -623/541 HST (-1.151564,-1.151548) -813/706 HST (-1.151570,-1.151525) -1079/937 HST (-1.151529,-1.151501) -38/33 EXTENDED HST (-1.151510,-1.151483) -1885/1637 HST (-1.151496,-1.151488) -1543/1340 HST (-1.151492,-1.151480) -1239/1076 HST (-1.151486,-1.151472) -973/845 HST (-1.151478,-1.151458) -745/647 HST (-1.151467,-1.151445) -593/515 HST (-1.151453,-1.151418) -479/416 HST (-1.151437,-1.151402) -365/317 HST (-1.151417,-1.151373) -289/251 HST (-1.151390,-1.151309) -175/152 HST (-1.151312,-1.151288) -662/575 HST (-1.151303,-1.151220) -137/119 HST (-1.151344,-1.151093) -236/205 HST (-1.151166,-1.151160) -99/86 EXTENDED HST (-1.151124,-1.151038) -160/139 HST (-1.151194,-1.150924) -282/245 HST (-1.151019,-1.150878) -61/53 HST (-1.151007,-1.150641) -206/179 HST (-1.150795,-1.150792) -145/126 EXTENDED HST (-1.150741,-1.150637) -84/73 HST (-1.150706,-1.150548) -275/239 HST (-1.150603,-1.150602) -191/166 EXTENDED HST (-1.150561,-1.150516) -107/93 HST (-1.150538,-1.150376) -130/113 HST (-1.150387,-1.150365) -153/133 HST (-1.150411,-1.150320) -635/552 HST (-1.150358,-1.150358) -482/419 EXTENDED HST (-1.150350,-1.150349) -329/286 EXTENDED HST (-1.150339,-1.150315) -176/153 HST (-1.150359,-1.150268) -551/479 HST (-1.150307,-1.150307) -375/326 EXTENDED HST (-1.150296,-1.150283) -199/173 HST (-1.150270,-1.150266) -643/559 HST (-1.150290,-1.150240) -865/752 HST (-1.150259,-1.150259) -222/193 EXTENDED HST (-1.150248,-1.150230) -1202/1045 HST (-1.150239,-1.150230) -245/213 HST (-1.150266,-1.150188) -758/659 HST (-1.150224,-1.150224) -513/446 EXTENDED HST (-1.150220,-1.150210) -268/233 HST (-1.150306,-1.150037) -314/273 HST (-1.150077,-1.149926) -23/20 EXTENDED HST (-1.149954,-1.149859) -606/527 HST (-1.149905,-1.149742) -330/287 HST (-1.149813,-1.148832) -54/47 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: 7433 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=(2,26)(3,25)(4,24)(5,23)(6,22)(7,21)(8,20)(9,19)(10,18)(11,17)(12,16)(13,15)", "b=(1,26)(2,25)(3,24)(4,23)(5,22)(6,21)(7,20)(8,19)(9,18)(10,17)(11,16)(12,15)(13,14)", "c=(1,26)(2,25)(3,24)(4,23)(5,22)(6,21)(7,20)(8,19)(9,18)(10,17)(11,16)(12,15)(13,14)", "d=<1,a*b,a*b,a*b,a*b,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,c,c*d,c*d,c*d,c*d,c*d>(2,26)(3,25)(4,24)(5,23)(6,22)(7,21)(8,20)(9,19)(10,18)(11,17)(12,16)(13,15)", "a*b*c*d"); When the translation term of the affine map is lambda1: NewSphereMachine( "a=(1,2)(3,26)(4,25)(5,24)(6,23)(7,22)(8,21)(9,20)(10,19)(11,18)(12,17)(13,16)(14,15)", "b=(2,26)(3,25)(4,24)(5,23)(6,22)(7,21)(8,20)(9,19)(10,18)(11,17)(12,16)(13,15)", "c=<1,a*b,a*b,a*b,a*b,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,c,c*d,c*d,c*d,c*d,c*d>(2,26)(3,25)(4,24)(5,23)(6,22)(7,21)(8,20)(9,19)(10,18)(11,17)(12,16)(13,15)", "d=<1,1,a*b,a*b,a*b,a*b,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c,c*d,c*d,c*d,c*d>(1,2)(3,26)(4,25)(5,24)(6,23)(7,22)(8,21)(9,20)(10,19)(11,18)(12,17)(13,16)(14,15)", "a*b*c*d"); When the translation term of the affine map is lambda2: NewSphereMachine( "a=(1,25)(2,24)(3,23)(4,22)(5,21)(6,20)(7,19)(8,18)(9,17)(10,16)(11,15)(12,14)", "b=(1,26)(2,25)(3,24)(4,23)(5,22)(6,21)(7,20)(8,19)(9,18)(10,17)(11,16)(12,15)(13,14)", "c=(1,26)(2,25)(3,24)(4,23)(5,22)(6,21)(7,20)(8,19)(9,18)(10,17)(11,16)(12,15)(13,14)", "d=(1,25)(2,24)(3,23)(4,22)(5,21)(6,20)(7,19)(8,18)(9,17)(10,16)(11,15)(12,14)", "a*b*c*d"); When the translation term of the affine map is lambda1+lambda2: NewSphereMachine( "a=(1,26)(2,25)(3,24)(4,23)(5,22)(6,21)(7,20)(8,19)(9,18)(10,17)(11,16)(12,15)(13,14)", "b=<1,a*b,a*b,a*b,a*b,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,c,c*d,c*d,c*d,c*d,c*d>(2,26)(3,25)(4,24)(5,23)(6,22)(7,21)(8,20)(9,19)(10,18)(11,17)(12,16)(13,15)", "c=(2,26)(3,25)(4,24)(5,23)(6,22)(7,21)(8,20)(9,19)(10,18)(11,17)(12,16)(13,15)", "d=(1,26)(2,25)(3,24)(4,23)(5,22)(6,21)(7,20)(8,19)(9,18)(10,17)(11,16)(12,15)(13,14)", "a*b*c*d");