These Thurston maps are NET maps for every choice of translation term. They are primitive and have degree 40. ALL THURSTON MULTIPLIERS c/d IN UNREDUCED FORM 0/1, 0/5, 0/8, 0/10, 0/40, 1/40, 1/20, 1/10, 1/8, 1/5, 1/4, 2/5, 1/2, 2/4 1/1, 2/2, 4/4, 2/1, 5/2, 6/2, 7/2, 4/1, 5/1, 6/1, 7/1, 14/2, 9/1, 11/1, 12/1 15/1, 17/1, 22/1, 34/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-73.892826,-1.017539) ( -0.983162,-0.016838) ( 0.016838,70.798990) The half-space computation does not determine rationality. EXCLUDED INTERVALS FOR JUST THE SUPPLEMENTAL HALF-SPACE COMPUTATION INTERVAL COMPUTED FOR HST OR EXTENDED HST (-164.152923,-103.426024) -128/1 HST (-132.664737,-84.177368 ) -103/1 HST (-106.328580,-68.197736 ) -84/1 HST ( -1.158073,-0.841853 ) -1/1 EXTENDED HST ( -0.019201,-0.014106 ) -1/60 HST ( -0.014226,-0.013946 ) -1/71 HST ( -0.016085,-0.011693 ) -1/72 HST ( -0.012052,-0.011313 ) -5/428 HST ( -0.011676,-0.011580 ) -1/86 HST ( -0.011316,-0.011157 ) -1/89 HST ( -0.012868,-0.009354 ) -1/90 HST ( -0.009365,-0.009326 ) -1/107 HST ( -0.010723,-0.007795 ) -1/108 HST ( -0.008909,-0.006476 ) -1/129 HST ( -0.007520,-0.005467 ) -2/309 HST ( -0.006461,-0.006442 ) -1/155 HST ( -0.005471,-0.005458 ) -1/183 HST ( -0.006294,-0.004575 ) -1/184 HST ( -0.004814,-0.004332 ) -3/656 HST ( -0.004571,-0.004562 ) -1/219 HST ( -0.004342,-0.004316 ) -1/231 HST ( -0.004992,-0.003629 ) -1/232 HST ( -0.003953,0.003953 ) 0/1 EXTENDED HST ( 0.003867,0.005305 ) 1/218 HST ( 0.004604,0.004613 ) 1/217 HST ( 0.004626,0.006363 ) 1/182 HST ( 0.005518,0.005532 ) 1/181 HST ( 0.005539,0.007619 ) 1/152 HST ( 0.006595,0.006650 ) 1/151 HST ( 0.006665,0.009215 ) 1/126 HST ( 0.007942,0.010926 ) 1/106 HST ( 0.009504,0.009544 ) 1/105 HST ( 0.009583,0.009648 ) 1/104 HST ( 0.009649,0.009769 ) 1/103 HST ( 0.009789,0.013466 ) 1/86 HST ( 0.011693,0.016085 ) 1/72 HST ( 0.014031,0.019302 ) 1/60 HST ( 70.367544,71.632456 ) 71/1 HST ( 59.659688,94.024522 ) 72/1 HST ( 70.230447,143.769553 ) 95/1 HST -128.490234)(130.491211 infinity EXTENDED HST The supplemental half-space computation shows that these NET maps are rational. SLOPE FUNCTION INFORMATION NUMBER OF FIXED POINTS: 1 EQUATOR? FIXED POINT c d 0 lambda1 lambda2 lambda1+lambda2 0/1 1 40 Yes Yes No No NUMBER OF EQUATORS: 1 1 0 0 There are no more slope function fixed points. Number of excluded intervals computed by the fixed point finder: 9988 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 either one of the above cycles or 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. 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=<1,b,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1>(2,40)(3,39)(4,38)(5,37)(6,36)(7,35)(8,34)(9,33)(10,32)(11,31)(12,30)(13,29)(14,28)(15,27)(16,26)(17,25)(18,24)(19,23)(20,22)", "b=(1,40)(2,39)(3,38)(4,37)(5,36)(6,35)(7,34)(8,33)(9,32)(10,31)(11,30)(12,29)(13,28)(14,27)(15,26)(16,25)(17,24)(18,23)(19,22)(20,21)", "c=<1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c,c*d>(2,40)(3,39)(4,38)(5,37)(6,36)(7,35)(8,34)(9,33)(10,32)(11,31)(12,30)(13,29)(14,28)(15,27)(16,26)(17,25)(18,24)(19,23)(20,22)", "d=<1,1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c>(1,2)(3,40)(4,39)(5,38)(6,37)(7,36)(8,35)(9,34)(10,33)(11,32)(12,31)(13,30)(14,29)(15,28)(16,27)(17,26)(18,25)(19,24)(20,23)(21,22)", "a*b*c*d"); When the translation term of the affine map is lambda1: NewSphereMachine( "a=(1,40)(2,39)(3,38)(4,37)(5,36)(6,35)(7,34)(8,33)(9,32)(10,31)(11,30)(12,29)(13,28)(14,27)(15,26)(16,25)(17,24)(18,23)(19,22)(20,21)", "b=(1,39)(2,38)(3,37)(4,36)(5,35)(6,34)(7,33)(8,32)(9,31)(10,30)(11,29)(12,28)(13,27)(14,26)(15,25)(16,24)(17,23)(18,22)(19,21)", "c=(1,40)(2,39)(3,38)(4,37)(5,36)(6,35)(7,34)(8,33)(9,32)(10,31)(11,30)(12,29)(13,28)(14,27)(15,26)(16,25)(17,24)(18,23)(19,22)(20,21)", "d=<1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c,c*d>(2,40)(3,39)(4,38)(5,37)(6,36)(7,35)(8,34)(9,33)(10,32)(11,31)(12,30)(13,29)(14,28)(15,27)(16,26)(17,25)(18,24)(19,23)(20,22)", "a*b*c*d"); When the translation term of the affine map is lambda2: NewSphereMachine( "a=(1,40)(2,39)(3,38)(4,37)(5,36)(6,35)(7,34)(8,33)(9,32)(10,31)(11,30)(12,29)(13,28)(14,27)(15,26)(16,25)(17,24)(18,23)(19,22)(20,21)", "b=<1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c,c*d>(2,40)(3,39)(4,38)(5,37)(6,36)(7,35)(8,34)(9,33)(10,32)(11,31)(12,30)(13,29)(14,28)(15,27)(16,26)(17,25)(18,24)(19,23)(20,22)", "c=(1,40)(2,39)(3,38)(4,37)(5,36)(6,35)(7,34)(8,33)(9,32)(10,31)(11,30)(12,29)(13,28)(14,27)(15,26)(16,25)(17,24)(18,23)(19,22)(20,21)", "d=(1,39)(2,38)(3,37)(4,36)(5,35)(6,34)(7,33)(8,32)(9,31)(10,30)(11,29)(12,28)(13,27)(14,26)(15,25)(16,24)(17,23)(18,22)(19,21)", "a*b*c*d"); When the translation term of the affine map is lambda1+lambda2: NewSphereMachine( "a=(1,39)(2,38)(3,37)(4,36)(5,35)(6,34)(7,33)(8,32)(9,31)(10,30)(11,29)(12,28)(13,27)(14,26)(15,25)(16,24)(17,23)(18,22)(19,21)", "b=(1,40)(2,39)(3,38)(4,37)(5,36)(6,35)(7,34)(8,33)(9,32)(10,31)(11,30)(12,29)(13,28)(14,27)(15,26)(16,25)(17,24)(18,23)(19,22)(20,21)", "c=(1,39)(2,38)(3,37)(4,36)(5,35)(6,34)(7,33)(8,32)(9,31)(10,30)(11,29)(12,28)(13,27)(14,26)(15,25)(16,24)(17,23)(18,22)(19,21)", "d=<1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,b^-1*a*b,1>(1,38)(2,37)(3,36)(4,35)(5,34)(6,33)(7,32)(8,31)(9,30)(10,29)(11,28)(12,27)(13,26)(14,25)(15,24)(16,23)(17,22)(18,21)(19,20)(39,40)", "a*b*c*d");