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 0/5, 0/20, 0/40, 1/10, 1/8, 1/5, 1/4, 2/8, 2/5, 1/2, 2/4, 3/5, 1/1, 2/2 2/1, 6/2, 6/1, 7/1, 13/1, 14/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-infinity,1.970588 ) ( 2.000000,85.023799) The half-space computation does not determine rationality. EXCLUDED INTERVALS FOR JUST THE SUPPLEMENTAL HALF-SPACE COMPUTATION INTERVAL COMPUTED FOR HST OR EXTENDED HST (-407.028824,-155.471176) -225/1 HST (-155.820237,-154.751192) -466/3 HST (-155.024999,-154.974999) -155/1 EXTENDED HST (-186.676903,-130.290839) -154/1 HST (-233.363192,-89.136808 ) -130/1 HST ( -89.632456,-88.367544 ) -89/1 HST (-107.289508,-75.355653 ) -88/1 HST ( -75.820237,-74.751192 ) -226/3 HST ( -75.024999,-74.974999 ) -75/1 EXTENDED HST ( -89.497924,-62.308528 ) -74/1 HST ( -73.428475,-54.116979 ) -62/1 HST ( -65.203179,-45.312950 ) -54/1 HST ( -45.316228,-44.683772 ) -45/1 EXTENDED HST -> HST ( -53.055807,-36.815161 ) -44/1 EXTENDED HST -> HST ( -40.146159,-33.327092 ) -73/2 HST ( -36.500000,-35.500000 ) -36/1 EXTENDED HST -> HST ( -59.697561,-22.802439 ) -33/1 EXTENDED HST -> HST ( -26.245831,-19.435987 ) -22/1 EXTENDED HST -> HST ( -22.687376,-15.570688 ) -19/1 EXTENDED HST -> HST ( -30.753289,-11.746711 ) -15/1 EXTENDED HST -> HST ( -11.764793,-11.663778 ) -82/7 HST ( -11.707107,-10.292893 ) -11/1 EXTENDED HST -> HST ( -11.433076,-9.443328 ) -10/1 EXTENDED HST -> HST ( -9.632456,-8.367544 ) -9/1 EXTENDED HST -> HST ( -10.110529,-7.373342 ) -8/1 EXTENDED HST -> HST ( -8.142857,-6.555556 ) -22/3 EXTENDED HST -> HST ( -7.024999,-6.974999 ) -7/1 EXTENDED HST ( -7.442848,-5.511698 ) -13/2 EXTENDED HST -> HST ( -6.500000,-5.500000 ) -6/1 EXTENDED HST -> HST ( -5.505536,-5.494488 ) -11/2 EXTENDED HST ( -5.615385,-5.000000 ) -16/3 EXTENDED HST -> HST ( -5.316228,-4.683772 ) -5/1 EXTENDED HST -> HST ( -4.769114,-4.144466 ) -9/2 EXTENDED HST -> HST ( -4.269493,-3.992738 ) -29/7 EXTENDED HST -> HST ( -4.036843,-3.124447 ) -4/1 EXTENDED HST -> HST ( -infinity,-0.500000 ) -3/1 EXTENDED HST -> HST ( -0.520802,-0.351626 ) -1/2 EXTENDED HST -> HST ( -0.374002,-0.213627 ) -1/3 EXTENDED HST -> HST ( -0.281019,-0.128620 ) -1/5 EXTENDED HST -> HST ( -0.195094,-0.038157 ) -1/8 EXTENDED HST -> HST ( -0.058824,-0.018868 ) -1/27 EXTENDED HST -> HST ( -0.024984,-0.012825 ) -1/53 HST ( -0.017164,-0.008844 ) -1/78 HST ( -0.010400,-0.007231 ) -1/114 HST ( -0.007969,0.007844 ) 0/1 EXTENDED HST ( 0.000000,0.100000 ) 1/18 EXTENDED HST -> HST ( 0.057722,0.213883 ) 1/7 EXTENDED HST -> HST ( 0.142857,0.333333 ) 1/4 EXTENDED HST -> HST ( 0.254780,0.396905 ) 1/3 EXTENDED HST -> HST ( 0.384615,0.466667 ) 2/5 EXTENDED HST -> HST ( 0.449791,0.491385 ) 7/15 EXTENDED HST -> HST ( 0.483946,0.499105 ) 29/59 HST ( 0.495581,0.504419 ) 1/2 EXTENDED HST ( 0.484069,0.592854 ) 6/11 EXTENDED HST -> HST ( 0.548816,0.784518 ) 2/3 EXTENDED HST -> HST ( 0.727273,0.909091 ) 4/5 EXTENDED HST -> HST ( 0.899294,0.926793 ) 10/11 EXTENDED HST -> HST ( 0.895881,0.950273 ) 13/14 EXTENDED HST -> HST ( 0.901195,1.013195 ) 20/21 EXTENDED HST -> HST ( 0.975610,1.025642 ) 1/1 EXTENDED HST ( 0.912813,1.239273 ) 21/20 EXTENDED HST -> HST ( 1.051543,1.124839 ) 12/11 EXTENDED HST -> HST ( 1.092350,1.193365 ) 8/7 EXTENDED HST -> HST ( 1.157616,1.445689 ) 4/3 EXTENDED HST -> HST ( 1.424889,1.607369 ) 3/2 EXTENDED HST -> HST ( 1.580179,1.783458 ) 5/3 EXTENDED HST -> HST ( 1.722222,1.833333 ) 9/5 EXTENDED HST -> HST ( 1.778502,1.953457 ) 11/6 EXTENDED HST -> HST ( 1.939448,1.970136 ) 43/22 EXTENDED HST -> HST ( 1.959173,1.984002 ) 67/34 HST ( 1.979107,1.989146 ) 125/63 HST ( 1.985344,1.992946 ) 185/93 HST ( 1.991239,2.008918 ) 2/1 EXTENDED HST ( 73.656096,104.860033 ) 86/1 HST ( 91.547415,122.707002 ) 839/8 HST ( 104.975001,105.025001 ) 105/1 EXTENDED HST ( 122.683772,123.316228 ) 123/1 HST ( 118.110988,129.125802 ) 247/2 HST ( 123.500000,124.500000 ) 124/1 HST ( 112.715031,152.557697 ) 130/1 HST ( 135.666667,174.714286 ) 458/3 HST ( 152.975001,153.025001 ) 153/1 EXTENDED HST ( 120.922026,316.577974 ) 175/1 HST -225.273438)(227.274414 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: 27235 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,c^-1,c,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>(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)", "b=<1,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>(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)", "c=<1,b,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>(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)", "d=(1,3)(2,5)(4,7)(6,9)(8,11)(10,13)(12,15)(14,17)(16,19)(18,21)(20,23)(22,25)(24,27)(26,29)(28,31)(30,33)(32,35)(34,37)(36,39)(38,40)", "a*b*c*d"); When the translation term of the affine map is lambda1: NewSphereMachine( "a=(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)", "b=<1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1>(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)", "c=(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)", "d=(1,4)(3,6)(5,8)(7,10)(9,12)(11,14)(13,16)(15,18)(17,20)(19,22)(21,24)(23,26)(25,28)(27,30)(29,32)(31,34)(33,36)(35,38)(37,40)", "a*b*c*d"); When the translation term of the affine map is lambda2: NewSphereMachine( "a=(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)", "b=<1,b,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>(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)", "c=<1,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>(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)", "d=(1,4)(3,6)(5,8)(7,10)(9,12)(11,14)(13,16)(15,18)(17,20)(19,22)(21,24)(23,26)(25,28)(27,30)(29,32)(31,34)(33,36)(35,38)(37,40)", "a*b*c*d"); When the translation term of the affine map is lambda1+lambda2: NewSphereMachine( "a=<1,b*d*a,b*c,1,b*c*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>(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)", "b=(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)", "c=<1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1>(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)", "d=(1,3)(2,5)(4,7)(6,9)(8,11)(10,13)(12,15)(14,17)(16,19)(18,21)(20,23)(22,25)(24,27)(26,29)(28,31)(30,33)(32,35)(34,37)(36,39)(38,40)", "a*b*c*d");