These Thurston maps are NET maps for every choice of translation term. They are primitive and have degree 30. 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 24. ALL THURSTON MULTIPLIERS c/d IN UNREDUCED FORM 0/1, 0/3, 0/5, 0/6, 0/10, 0/15, 0/30, 1/30, 1/10, 1/6, 1/2, 3/6, 4/5, 4/3 3/2, 5/2, 8/3, 6/2, 7/2, 4/1, 10/2, 6/1, 8/1, 10/1, 18/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-infinity,-0.156290) (-0.156189,-0.154927) (-0.154900,-0.133660) (-0.117394,-0.105467) (-0.094686,-0.092833) (-0.092443,-0.089425) (-0.089064,-0.087422) (-0.079610,-0.078296) (-0.078019,-0.075858) (-0.075598,-0.074412) (-0.068675,-0.067695) (-0.067488,-0.065865) (-0.065669,-0.064772) (-0.060382,-0.059623) (-0.059462,-0.058198) (-0.053142,-0.052131) (-0.048037,-0.047209) (-0.043826,-0.043136) (-0.040294,-0.039710) (-0.037289,-0.036788) (-0.034701,-0.034267) (-0.032449,-0.032069) (-0.030472,-0.030136) (-0.028721,-0.028423) (-0.027161,-0.026894) (-0.025762,-0.025522) (-0.024499,-0.024282) (-0.023355,-0.023157) (-0.022313,-0.022132) (-0.021360,-0.021194) (-0.020484,-0.020332) ( 0.020332,0.020484 ) ( 0.021194,0.021360 ) ( 0.022132,0.022313 ) ( 0.023157,0.023355 ) ( 0.024282,0.024499 ) ( 0.025522,0.025762 ) ( 0.026894,0.027161 ) ( 0.028423,0.028721 ) ( 0.030136,0.030472 ) ( 0.032069,0.032449 ) ( 0.034267,0.034701 ) ( 0.036788,0.037289 ) ( 0.039710,0.040294 ) ( 0.043136,0.043826 ) ( 0.047209,0.048037 ) ( 0.052131,0.053142 ) ( 0.058198,0.059462 ) ( 0.059623,0.060382 ) ( 0.064772,0.065669 ) ( 0.065865,0.067488 ) ( 0.067695,0.068675 ) ( 0.074412,0.075598 ) ( 0.075858,0.078019 ) ( 0.078296,0.079610 ) ( 0.087422,0.089064 ) ( 0.089425,0.092443 ) ( 0.092833,0.094686 ) ( 0.105467,0.117394 ) ( 0.133660,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 (-0.163404,-0.146667) -5/32 EXTENDED HST -> HST (-0.137121,-0.130166) -29/217 HST (-0.133521,-0.133146) -2/15 EXTENDED HST (-0.142726,-0.116623) -7/54 HST (-0.129155,-0.127993) -4/31 EXTENDED HST -> HST (-0.125095,-0.124905) -1/8 EXTENDED HST (-0.108182,-0.102731) -29/275 HST (-0.105380,-0.105146) -2/19 EXTENDED HST (-0.106127,-0.099245) -19/185 HST (-0.102642,-0.101907) -4/39 EXTENDED HST -> HST (-0.100061,-0.099939) -1/10 EXTENDED HST (-0.107097,-0.086850) -3/31 EXTENDED HST -> HST (-0.095362,-0.095115) -2/21 EXTENDED HST (-0.094408,-0.076354) -3/35 EXTENDED HST -> HST (-0.083376,-0.083291) -1/12 EXTENDED HST (-0.076578,-0.074955) -5/66 HST (-0.080420,-0.068279) -9/121 HST (-0.074132,-0.074016) -2/27 EXTENDED HST (-0.071460,-0.071398) -1/14 EXTENDED HST (-0.068219,-0.066928) -5/74 HST (-0.066407,-0.065183) -5/76 HST (-0.070010,-0.059440) -9/139 HST (-0.064560,-0.064472) -2/31 EXTENDED HST (-0.062524,-0.062476) -1/16 EXTENDED HST (-0.058622,-0.057665) -5/86 HST (-0.058045,-0.057344) -3/52 HST (-0.061986,-0.052628) -9/157 HST (-0.057177,-0.057108) -2/35 EXTENDED HST (-0.055574,-0.055537) -1/18 EXTENDED HST (-0.052470,-0.051703) -5/96 HST (-0.052008,-0.051444) -3/58 HST (-0.055612,-0.047216) -9/175 HST (-0.051310,-0.051254) -2/39 EXTENDED HST (-0.050015,-0.049985) -1/20 EXTENDED HST (-0.047487,-0.046857) -5/106 HST (-0.047108,-0.046645) -3/64 HST (-0.050427,-0.042814) -9/193 HST (-0.046534,-0.046489) -2/43 EXTENDED HST (-0.045467,-0.045442) -1/22 EXTENDED HST (-0.042885,-0.042586) -5/117 HST (-0.043669,-0.041501) -29/681 HST (-0.042572,-0.042534) -2/47 EXTENDED HST (-0.041677,-0.041656) -1/24 EXTENDED HST (-0.045687,-0.036574) -3/73 HST (-0.040839,-0.040794) -2/49 EXTENDED HST (-0.036605,-0.036388) -5/137 HST (-0.037311,-0.035462) -29/797 HST (-0.036378,-0.036350) -2/55 EXTENDED HST (-0.035722,-0.035707) -1/28 EXTENDED HST (-0.039256,-0.031384) -3/85 HST (-0.035104,-0.035071) -2/57 EXTENDED HST (-0.033001,-0.029777) -8/255 HST (-0.031256,-0.031244) -1/32 EXTENDED HST (-0.032987,-0.026337) -3/101 HST (-0.029417,-0.029407) -1/34 EXTENDED HST (-0.027842,-0.024829) -33/1253 HST (-0.026320,-0.026312) -1/38 EXTENDED HST (-0.027600,-0.022012) -3/121 HST (-0.024700,-0.024683) -2/81 EXTENDED HST (-0.023799,-0.020206) -9/409 HST (-0.021983,-0.021973) -2/91 EXTENDED HST (-0.021742,-0.021736) -1/46 EXTENDED HST (-0.050834,0.056596 ) 0/1 EXTENDED HST ( 0.049650,0.063435 ) 3/53 HST ( 0.057108,0.057177 ) 2/35 EXTENDED HST ( 0.055928,0.071575 ) 3/47 EXTENDED HST -> HST ( 0.064472,0.064560 ) 2/31 EXTENDED HST ( 0.064025,0.082113 ) 3/41 EXTENDED HST -> HST ( 0.074016,0.074132 ) 2/27 EXTENDED HST ( 0.077890,0.086835 ) 6/73 HST ( 0.083291,0.083376 ) 1/12 EXTENDED HST ( 0.086770,0.086914 ) 33/380 HST ( 0.086877,0.087036 ) 2/23 EXTENDED HST ( 0.079077,0.095834 ) 9/103 HST ( 0.084925,0.109526 ) 3/31 EXTENDED HST -> HST ( 0.099939,0.100061 ) 1/10 EXTENDED HST ( 0.114537,0.120277 ) 29/247 HST ( 0.117501,0.117793 ) 2/17 EXTENDED HST ( 0.105108,0.136290 ) 7/58 HST ( 0.121104,0.122144 ) 4/33 EXTENDED HST -> HST ( 0.124905,0.125095 ) 1/8 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: 9664 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=(2,30)(3,29)(4,28)(5,27)(6,26)(7,25)(8,24)(9,23)(10,22)(11,21)(12,20)(13,19)(14,18)(15,17)", "b=(1,30)(2,29)(3,28)(4,27)(5,26)(6,25)(7,24)(8,23)(9,22)(10,21)(11,20)(12,19)(13,18)(14,17)(15,16)", "c=(1,30)(2,29)(3,28)(4,27)(5,26)(6,25)(7,24)(8,23)(9,22)(10,21)(11,20)(12,19)(13,18)(14,17)(15,16)", "d=<1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c,c,c,c,c,c,c>(2,30)(3,29)(4,28)(5,27)(6,26)(7,25)(8,24)(9,23)(10,22)(11,21)(12,20)(13,19)(14,18)(15,17)", "a*b*c*d"); When the translation term of the affine map is lambda1: NewSphereMachine( "a=(1,2)(3,30)(4,29)(5,28)(6,27)(7,26)(8,25)(9,24)(10,23)(11,22)(12,21)(13,20)(14,19)(15,18)(16,17)", "b=(2,30)(3,29)(4,28)(5,27)(6,26)(7,25)(8,24)(9,23)(10,22)(11,21)(12,20)(13,19)(14,18)(15,17)", "c=<1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c,c,c,c,c,c,c>(2,30)(3,29)(4,28)(5,27)(6,26)(7,25)(8,24)(9,23)(10,22)(11,21)(12,20)(13,19)(14,18)(15,17)", "d=<1,d,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c,c,c,c,c,c>(1,2)(3,30)(4,29)(5,28)(6,27)(7,26)(8,25)(9,24)(10,23)(11,22)(12,21)(13,20)(14,19)(15,18)(16,17)", "a*b*c*d"); When the translation term of the affine map is lambda2: NewSphereMachine( "a=(1,29)(2,28)(3,27)(4,26)(5,25)(6,24)(7,23)(8,22)(9,21)(10,20)(11,19)(12,18)(13,17)(14,16)", "b=(1,30)(2,29)(3,28)(4,27)(5,26)(6,25)(7,24)(8,23)(9,22)(10,21)(11,20)(12,19)(13,18)(14,17)(15,16)", "c=(1,30)(2,29)(3,28)(4,27)(5,26)(6,25)(7,24)(8,23)(9,22)(10,21)(11,20)(12,19)(13,18)(14,17)(15,16)", "d=(1,29)(2,28)(3,27)(4,26)(5,25)(6,24)(7,23)(8,22)(9,21)(10,20)(11,19)(12,18)(13,17)(14,16)", "a*b*c*d"); When the translation term of the affine map is lambda1+lambda2: NewSphereMachine( "a=(1,30)(2,29)(3,28)(4,27)(5,26)(6,25)(7,24)(8,23)(9,22)(10,21)(11,20)(12,19)(13,18)(14,17)(15,16)", "b=<1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c,c,c,c,c,c,c>(2,30)(3,29)(4,28)(5,27)(6,26)(7,25)(8,24)(9,23)(10,22)(11,21)(12,20)(13,19)(14,18)(15,17)", "c=(2,30)(3,29)(4,28)(5,27)(6,26)(7,25)(8,24)(9,23)(10,22)(11,21)(12,20)(13,19)(14,18)(15,17)", "d=(1,30)(2,29)(3,28)(4,27)(5,26)(6,25)(7,24)(8,23)(9,22)(10,21)(11,20)(12,19)(13,18)(14,17)(15,16)", "a*b*c*d");