These Thurston maps are NET maps for every choice of translation term. They are primitive and have degree 24. 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 12. ALL THURSTON MULTIPLIERS c/d IN UNREDUCED FORM 0/1, 0/2, 0/3, 0/4, 0/6, 0/8, 0/12, 0/24, 1/24, 1/8, 2/6, 2/3, 2/2, 4/4 2/1, 6/3, 10/2, 10/1, 14/1, 22/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-infinity,-0.094895) (-0.094797,-0.087327) (-0.079689,-0.078220) (-0.078150,-0.075734) (-0.075669,-0.074343) (-0.068734,-0.067638) (-0.067586,-0.065772) (-0.065723,-0.064720) (-0.060427,-0.059579) (-0.059538,-0.058126) (-0.053203,-0.052072) (-0.048086,-0.047161) (-0.043868,-0.043096) (-0.040329,-0.039676) (-0.037319,-0.036759) (-0.034727,-0.034242) (-0.032472,-0.032047) (-0.030492,-0.030117) (-0.028739,-0.028406) (-0.027177,-0.026879) (-0.025776,-0.025508) (-0.024512,-0.024269) (-0.023367,-0.023146) (-0.022323,-0.022122) (-0.021369,-0.021185) (-0.020494,-0.020323) ( 0.020323,0.020494 ) ( 0.021185,0.021369 ) ( 0.022122,0.022323 ) ( 0.023146,0.023367 ) ( 0.024269,0.024512 ) ( 0.025508,0.025776 ) ( 0.026879,0.027177 ) ( 0.028406,0.028739 ) ( 0.030117,0.030492 ) ( 0.032047,0.032472 ) ( 0.034242,0.034727 ) ( 0.036759,0.037319 ) ( 0.039676,0.040329 ) ( 0.043096,0.043868 ) ( 0.047161,0.048086 ) ( 0.052072,0.053203 ) ( 0.058126,0.059538 ) ( 0.059579,0.060427 ) ( 0.064720,0.065723 ) ( 0.065772,0.067586 ) ( 0.067638,0.068734 ) ( 0.074343,0.075669 ) ( 0.075734,0.078150 ) ( 0.078220,0.079689 ) ( 0.087327,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 (-0.095032,-0.094749) -11/116 HST (-0.087368,-0.087129) -11/126 HST (-0.095575,-0.078629) -23/264 HST (-0.087068,-0.086845) -2/23 EXTENDED HST (-0.083392,-0.083274) -1/12 EXTENDED HST (-0.078255,-0.078124) -14/179 HST (-0.075759,-0.075636) -14/185 HST (-0.074372,-0.074199) -11/148 HST (-0.081403,-0.066956) -23/310 HST (-0.074155,-0.073993) -2/27 EXTENDED HST (-0.071472,-0.071385) -1/14 EXTENDED HST (-0.065790,-0.065698) -14/213 HST (-0.064742,-0.064611) -11/170 HST (-0.070892,-0.058301) -23/356 HST (-0.064578,-0.064455) -2/31 EXTENDED HST (-0.062533,-0.062467) -1/16 EXTENDED HST (-0.058140,-0.058068) -14/241 HST (-0.058087,-0.057303) -3/52 HST (-0.057320,-0.057217) -11/192 HST (-0.062784,-0.051627) -23/402 HST (-0.057191,-0.057095) -2/35 EXTENDED HST (-0.055582,-0.055529) -1/18 EXTENDED HST (-0.055638,-0.047437) -5/97 HST (-0.051321,-0.051243) -2/39 EXTENDED HST (-0.050021,-0.049979) -1/20 EXTENDED HST (-0.047170,-0.047123) -14/297 HST (-0.047135,-0.046617) -3/64 HST (-0.046629,-0.046561) -11/236 HST (-0.051097,-0.042009) -23/494 HST (-0.046544,-0.046480) -2/43 EXTENDED HST (-0.045472,-0.045437) -1/22 EXTENDED HST (-0.044307,-0.039520) -6/143 HST (-0.041681,-0.041652) -1/24 EXTENDED HST (-0.039658,-0.039291) -3/76 HST (-0.039299,-0.039251) -11/280 HST (-0.043078,-0.035412) -23/586 HST (-0.039238,-0.039193) -2/51 EXTENDED HST (-0.038474,-0.038449) -1/26 EXTENDED HST (-0.037659,-0.032248) -2/57 HST (-0.032052,-0.032029) -14/437 HST (-0.032035,-0.031795) -3/94 HST (-0.031801,-0.031769) -11/346 HST (-0.034870,-0.028661) -23/724 HST (-0.031761,-0.031731) -2/63 EXTENDED HST (-0.031258,-0.031242) -1/32 EXTENDED HST (-0.028409,-0.028392) -14/493 HST (-0.028397,-0.028208) -3/106 HST (-0.028212,-0.028187) -11/390 HST (-0.030939,-0.025429) -23/816 HST (-0.028181,-0.028157) -2/71 EXTENDED HST (-0.027784,-0.027771) -1/36 EXTENDED HST (-0.025500,-0.025348) -3/118 HST (-0.025351,-0.025331) -11/434 HST (-0.027805,-0.022852) -23/908 HST (-0.025326,-0.025307) -2/79 EXTENDED HST (-0.025005,-0.024995) -1/40 EXTENDED HST (-0.024626,-0.021026) -5/219 HST (-0.022732,-0.022723) -1/44 EXTENDED HST (-0.022571,-0.019262) -3/143 HST (-0.020837,-0.020830) -1/48 EXTENDED HST (-0.078437,0.093057 ) 0/1 EXTENDED 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: 3494 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 |q'| <= |q| 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=(2,24)(3,23)(4,22)(5,21)(6,20)(7,19)(8,18)(9,17)(10,16)(11,15)(12,14)", "b=(1,24)(2,23)(3,22)(4,21)(5,20)(6,19)(7,18)(8,17)(9,16)(10,15)(11,14)(12,13)", "c=(1,24)(2,23)(3,22)(4,21)(5,20)(6,19)(7,18)(8,17)(9,16)(10,15)(11,14)(12,13)", "d=<1,c^-1,c^-1,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,c,c,c,c,c>(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: NewSphereMachine( "a=(1,2)(3,24)(4,23)(5,22)(6,21)(7,20)(8,19)(9,18)(10,17)(11,16)(12,15)(13,14)", "b=(2,24)(3,23)(4,22)(5,21)(6,20)(7,19)(8,18)(9,17)(10,16)(11,15)(12,14)", "c=<1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,c,c,c,c,c,c>(2,24)(3,23)(4,22)(5,21)(6,20)(7,19)(8,18)(9,17)(10,16)(11,15)(12,14)", "d=<1,d,c^-1,c^-1,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,c,c,c,c,c>(1,2)(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"); When the translation term of the affine map is lambda2: NewSphereMachine( "a=(1,23)(2,22)(3,21)(4,20)(5,19)(6,18)(7,17)(8,16)(9,15)(10,14)(11,13)", "b=(1,24)(2,23)(3,22)(4,21)(5,20)(6,19)(7,18)(8,17)(9,16)(10,15)(11,14)(12,13)", "c=(1,24)(2,23)(3,22)(4,21)(5,20)(6,19)(7,18)(8,17)(9,16)(10,15)(11,14)(12,13)", "d=(1,23)(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 lambda1+lambda2: NewSphereMachine( "a=(1,24)(2,23)(3,22)(4,21)(5,20)(6,19)(7,18)(8,17)(9,16)(10,15)(11,14)(12,13)", "b=<1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,c,c,c,c,c,c>(2,24)(3,23)(4,22)(5,21)(6,20)(7,19)(8,18)(9,17)(10,16)(11,15)(12,14)", "c=(2,24)(3,23)(4,22)(5,21)(6,20)(7,19)(8,18)(9,17)(10,16)(11,15)(12,14)", "d=(1,24)(2,23)(3,22)(4,21)(5,20)(6,19)(7,18)(8,17)(9,16)(10,15)(11,14)(12,13)", "a*b*c*d");