These Thurston maps are NET maps for every choice of translation term. They have degree 26. They are imprimitive, each factoring as a NET map with degree 13 followed by a Euclidean NET map with degree 2. 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 12. ALL THURSTON MULTIPLIERS c/d IN UNREDUCED FORM 0/1, 0/13, 0/26, 1/2, 3/2, 2/1, 4/2, 5/2, 6/2, 7/2, 4/1, 6/1, 8/1, 10/1 12/1, 14/1, 16/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-infinity,-1.174458) (-1.147775,-1.146525) (-1.134173,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 (-1.180723,-1.169399) -27/23 EXTENDED HST -> HST (-1.170979,-1.167941) -76/65 HST (-1.174237,-1.164474) -153/131 HST (-1.166973,-1.166368) -7/6 EXTENDED HST (-1.164493,-1.160753) -43/37 EXTENDED HST -> HST (-1.161577,-1.159500) -36/31 EXTENDED HST -> HST (-1.160734,-1.156630) -22/19 EXTENDED HST -> HST (-1.156830,-1.156346) -96/83 HST (-1.156464,-1.156217) -392/339 HST (-1.156285,-1.156215) -37/32 EXTENDED HST (-1.156663,-1.155705) -422/365 HST (-1.156162,-1.155846) -126/109 HST (-1.155932,-1.155180) -52/45 EXTENDED HST (-1.155295,-1.154640) -67/58 HST (-1.154800,-1.154417) -112/97 HST (-1.154837,-1.154069) -157/136 HST (-1.154868,-1.153331) -412/357 HST (-1.153944,-1.153747) -15/13 EXTENDED HST (-1.154993,-1.151498) -113/98 HST (-1.152963,-1.146786) -23/20 EXTENDED HST -> HST (-1.146798,-1.146178) -180/157 HST (-1.146479,-1.145280) -47/41 EXTENDED HST -> HST (-1.146181,-1.143849) -71/62 HST (-1.144276,-1.143255) -167/146 HST (-1.143730,-1.141915) -8/7 EXTENDED HST (-1.142192,-1.140170) -89/78 HST (-1.140853,-1.133145) -25/22 EXTENDED HST -> 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. The union of the excluded intervals computed by the fixed point finder became a union of 10,000 disjoint intervals: the search for all slope function fixed points aborted. 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. If the slope function maps slope p/q to slope p'/q', then |p'| <= |p| for every slope p/q with |p| <= 50 and |q| <= 50. 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,a*b,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,c*d,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,a*b,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,c,c*d,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,a*b,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,c,c*d,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,a*b,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,c,c*d,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");