These Thurston maps are NET maps for every choice of translation term. They are primitive and have degree 28. ALL THURSTON MULTIPLIERS c/d IN UNREDUCED FORM 0/1, 0/7, 0/14, 0/28, 1/7, 1/4, 1/2, 2/4, 1/1, 3/2, 2/1, 4/2, 3/1, 5/1, 6/1 9/1, 13/1, 19/1, 25/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-13.528305,-1.059084) ( -1.058321,-1.056011) ( -1.050963,-1.049073) ( -1.048780,-1.046512) ( -1.037037,-1.034483) ( -1.028986,-1.028169) ( -1.028073,-1.027489) ( -1.024217,-1.023415) ( -1.022924,-1.022534) ( -1.020619,-1.020202) ( -0.979798,-0.979381) ( -0.977466,-0.977076) ( -0.976585,-0.975783) ( -0.972511,-0.971927) ( -0.971831,-0.971014) ( -0.965517,-0.962963) ( -0.959764,-0.958586) ( -0.953488,-0.951220) ( -0.950927,-0.949037) ( -0.943989,-0.941679) ( -0.939892,-0.505051) ( -0.494949,-0.060108) ( -0.058321,-0.056011) ( -0.050963,-0.049073) ( -0.048780,-0.046512) ( -0.041414,-0.040236) ( -0.037037,-0.034483) ( -0.028986,-0.028169) ( -0.028073,-0.027489) ( -0.024217,-0.023415) ( -0.022924,-0.022534) ( -0.020619,-0.020202) ( 0.020202,0.020619 ) ( 0.022534,0.022924 ) ( 0.023415,0.024217 ) ( 0.027489,0.028073 ) ( 0.028169,0.028986 ) ( 0.034483,0.037037 ) ( 0.040236,0.041414 ) ( 0.046512,0.048780 ) ( 0.049073,0.050963 ) ( 0.056011,0.058321 ) ( 0.059084,13.528305) The half-space computation does not determine rationality. EXCLUDED INTERVALS FOR JUST THE SUPPLEMENTAL HALF-SPACE COMPUTATION INTERVAL COMPUTED FOR HST OR EXTENDED HST ( -1.065436,-1.050060) -18/17 EXTENDED HST -> HST ( -1.051711,-1.044443) -43/41 EXTENDED HST -> HST ( -1.049954,-1.038346) -71/68 HST ( -1.043620,-1.042120) -24/23 EXTENDED HST -> HST ( -1.042225,-1.032775) -28/27 EXTENDED HST -> HST ( -1.036868,-1.028384) -32/31 EXTENDED HST -> HST ( -1.030688,-1.026149) -73/71 HST ( -1.029216,-1.022530) -40/39 EXTENDED HST -> HST ( -1.024838,-1.019280) -46/45 EXTENDED HST -> HST ( -1.019372,-1.019092) -53/52 HST ( -1.021212,-1.016311) -54/53 HST ( -1.018004,-1.013919) -63/62 HST ( -1.014580,-1.013250) -510/503 HST ( -1.013903,-1.013875) -73/72 EXTENDED HST ( -1.014975,-1.011609) -153/151 HST ( -1.013224,-1.013093) -77/76 HST ( -1.013011,-1.010070) -88/87 HST ( -1.011499,-1.008625) -201/199 HST ( -1.010038,-1.009962) -101/100 HST ( -1.008649,-1.008593) -117/116 HST ( -1.009596,-1.007449) -118/117 HST ( -1.008369,-1.006484) -271/269 HST ( -1.007412,-1.007367) -136/135 HST ( -1.007292,-1.005642) -156/155 HST ( -1.006311,-1.004885) -179/178 HST ( -1.005498,-1.004271) -823/819 HST ( -1.004878,-1.004878) -206/205 EXTENDED HST ( -1.004540,-0.995521) -1/1 EXTENDED HST ( -0.995656,-0.994411) -201/202 HST ( -0.995046,-0.993640) -175/176 HST ( -0.994295,-0.992663) -152/153 HST ( -0.993445,-0.991555) -133/134 HST ( -0.992535,-0.990424) -117/118 HST ( -0.991515,-0.989117) -103/104 HST ( -0.990314,-0.990205) -102/103 HST ( -0.990202,-0.987413) -89/90 HST ( -0.988773,-0.988670) -88/89 HST ( -0.988698,-0.985440) -77/78 HST ( -0.987097,-0.986928) -76/77 HST ( -0.986890,-0.983110) -66/67 HST ( -0.984863,-0.984834) -65/66 EXTENDED HST ( -0.984722,-0.980404) -56/57 HST ( -0.982238,-0.977234) -49/50 EXTENDED HST -> HST ( -0.979515,-0.973610) -42/43 EXTENDED HST -> HST ( -0.975365,-0.971451) -73/75 HST ( -0.972983,-0.972963) -36/37 EXTENDED HST ( -0.973680,-0.966348) -33/34 EXTENDED HST -> HST ( -0.970204,-0.961614) -28/29 EXTENDED HST -> HST ( -0.965327,-0.955773) -24/25 EXTENDED HST -> HST ( -0.959031,-0.947219) -21/22 EXTENDED HST -> HST ( -0.949207,-0.935508) -17/18 EXTENDED HST -> HST ( -0.509091,-0.491227) -1/2 EXTENDED HST ( -0.064492,-0.050793) -1/17 EXTENDED HST -> HST ( -0.051338,-0.044768) -2/41 EXTENDED HST -> HST ( -0.049401,-0.038775) -2/45 EXTENDED HST -> HST ( -0.043620,-0.042120) -1/23 EXTENDED HST -> HST ( -0.041829,-0.033088) -1/27 EXTENDED HST -> HST ( -0.036567,-0.028618) -1/31 EXTENDED HST -> HST ( -0.030557,-0.026262) -2/71 HST ( -0.029026,-0.022678) -1/39 EXTENDED HST -> HST ( -0.024701,-0.019387) -1/45 EXTENDED HST -> HST ( -0.020556,-0.018182) -5/258 HST ( -0.019372,-0.019092) -1/52 HST ( -0.020550,-0.016025) -1/55 HST ( -0.017932,-0.013975) -2/125 HST ( -0.016000,-0.015748) -1/63 HST ( -0.015652,-0.012216) -3/215 HST ( -0.013903,-0.013875) -1/72 EXTENDED HST ( -0.013579,-0.010605) -1/82 HST ( -0.011878,-0.009245) -1/95 HST ( -0.010299,-0.007994) -1/109 HST ( -0.008966,-0.006988) -4/501 HST ( -0.007981,-0.007892) -1/126 HST ( -0.007507,-0.006459) -7/1002 HST ( -0.006986,-0.006952) -2/287 HST ( -0.006949,-0.006940) -1/144 EXTENDED HST ( -0.007280,-0.005651) -1/155 HST ( -0.005658,-0.005621) -1/177 HST ( -0.006302,-0.004892) -1/178 HST ( -0.004899,-0.004886) -2/409 HST ( -0.005491,-0.004276) -4/819 HST ( -0.004878,-0.004878) -1/205 EXTENDED HST ( -0.004479,0.004520 ) 0/1 EXTENDED HST ( 0.004144,0.005351 ) 1/211 HST ( 0.004746,0.004778 ) 1/210 HST ( 0.004781,0.006168 ) 1/183 HST ( 0.005490,0.007070 ) 1/160 HST ( 0.006280,0.006326 ) 1/159 HST ( 0.006303,0.008120 ) 1/139 HST ( 0.007239,0.009326 ) 1/120 HST ( 0.008368,0.008439 ) 1/119 HST ( 0.008464,0.010909 ) 1/104 HST ( 0.009686,0.009795 ) 1/103 HST ( 0.009770,0.012622 ) 1/90 HST ( 0.011227,0.011330 ) 1/89 HST ( 0.011265,0.014608 ) 1/78 HST ( 0.012903,0.013072 ) 1/77 HST ( 0.013061,0.016954 ) 1/67 HST ( 0.015137,0.015166 ) 1/66 EXTENDED HST ( 0.015211,0.019683 ) 1/57 HST ( 0.017671,0.022883 ) 1/50 EXTENDED HST -> HST ( 0.020364,0.026547 ) 1/43 EXTENDED HST -> HST ( 0.024536,0.028664 ) 2/75 HST ( 0.027017,0.027037 ) 1/37 EXTENDED HST ( 0.026122,0.033908 ) 1/34 EXTENDED HST -> HST ( 0.029542,0.038719 ) 1/29 EXTENDED HST -> HST ( 0.034330,0.044669 ) 1/25 EXTENDED HST -> HST ( 0.040491,0.053412 ) 1/22 EXTENDED HST -> HST ( 0.050060,0.065436 ) 1/18 EXTENDED HST -> HST -10.582031)(9.583008 infinity 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: 24037 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. 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=(1,27)(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=(1,27)(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=(1,28)(2,27)(3,26)(4,25)(5,24)(6,23)(7,22)(8,21)(9,20)(10,19)(11,18)(12,17)(13,16)(14,15)", "d=(1,28)(2,27)(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 lambda1: NewSphereMachine( "a=<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>(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=(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)", "c=(1,28)(2,27)(3,26)(4,25)(5,24)(6,23)(7,22)(8,21)(9,20)(10,19)(11,18)(12,17)(13,16)(14,15)", "d=(1,28)(2,27)(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=(1,28)(2,27)(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=(1,28)(2,27)(3,26)(4,25)(5,24)(6,23)(7,22)(8,21)(9,20)(10,19)(11,18)(12,17)(13,16)(14,15)", "c=(1,27)(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=(1,27)(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+lambda2: NewSphereMachine( "a=(1,28)(2,27)(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=(1,28)(2,27)(3,26)(4,25)(5,24)(6,23)(7,22)(8,21)(9,20)(10,19)(11,18)(12,17)(13,16)(14,15)", "c=(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)", "d=<1,c^-1*b,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,b^-1*c>(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");