These Thurston maps are NET maps for every choice of translation term. They have degree 40. They are imprimitive, each factoring as a NET map with degree 20 followed by a Euclidean NET map with degree 2. ALL THURSTON MULTIPLIERS c/d IN UNREDUCED FORM 0/1, 0/5, 0/10, 0/20, 0/40, 1/8, 2/5, 2/4, 2/2, 2/1, 6/2, 4/1, 6/1, 12/1 22/1, 34/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-10.621784,-0.507072) ( -0.492760,0.492760 ) ( 0.507072,0.963123 ) ( 0.965862,0.967434 ) ( 0.971137,0.971714 ) ( 0.974084,0.975854 ) ( 0.977602,0.977951 ) ( 0.979713,0.980279 ) ( 1.022049,1.022398 ) ( 1.024146,1.025916 ) ( 1.028286,1.028863 ) ( 1.032566,1.034138 ) ( 1.036302,2.000000 ) ( 2.000000,10.469602) The half-space computation does not determine rationality. EXCLUDED INTERVALS FOR JUST THE SUPPLEMENTAL HALF-SPACE COMPUTATION INTERVAL COMPUTED FOR HST OR EXTENDED HST (-13.850058,-11.888636) -13/1 EXTENDED HST -> HST (-12.773967,-10.954677) -47/4 EXTENDED HST -> HST (-11.697875,-10.020718) -11/1 EXTENDED HST -> HST ( -0.510791,-0.503546 ) -36/71 HST ( -0.504459,-0.495619 ) -1/2 EXTENDED HST ( -0.496403,-0.489362 ) -35/71 HST ( 0.489362,0.496403 ) 35/71 HST ( 0.495619,0.504459 ) 1/2 EXTENDED HST ( 0.503546,0.510791 ) 36/71 HST ( 0.957481,0.969871 ) 27/28 EXTENDED HST -> HST ( 0.965284,0.977096 ) 33/34 EXTENDED HST -> HST ( 0.971638,0.982266 ) 43/44 EXTENDED HST -> HST ( 0.979597,0.985639 ) 56/57 HST ( 0.985569,0.985857 ) 69/70 HST ( 0.984479,0.987630 ) 70/71 HST ( 0.986332,0.989183 ) 80/81 HST ( 0.987302,0.991083 ) 92/93 HST ( 0.989556,0.992671 ) 112/113 HST ( 0.991453,0.994005 ) 136/137 HST ( 0.992982,0.995080 ) 166/167 HST ( 0.994757,1.005298 ) 1/1 EXTENDED HST ( 1.004342,1.006693 ) 182/181 HST ( 1.005525,1.005587 ) 181/180 HST ( 1.005574,1.007988 ) 149/148 HST ( 1.006780,1.006856 ) 147/146 HST ( 1.006868,1.008719 ) 130/129 HST ( 1.007756,1.011999 ) 102/101 HST ( 1.009957,1.014295 ) 83/82 HST ( 1.012329,1.015572 ) 72/71 HST ( 1.014273,1.020529 ) 59/58 HST ( 1.017328,1.026834 ) 47/46 EXTENDED HST -> HST ( 1.020711,1.033919 ) 37/36 EXTENDED HST -> HST ( 1.029744,1.043069 ) 29/28 EXTENDED HST -> HST ( 1.991200,2.008918 ) 2/1 EXTENDED HST ( 9.713175,11.191348 ) 21/2 EXTENDED HST -> HST ( 10.526383,11.976130 ) 11/1 EXTENDED HST -> HST ( 11.460342,13.052221 ) 12/1 EXTENDED HST -> HST ( 12.394301,14.128312 ) 53/4 HST ( 13.328260,15.204403 ) 14/1 EXTENDED HST -> HST -13.141602)(14.142578 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: 36389 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=(1,39)(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=(1,39)(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=(1,40)(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)", "a*b*c*d"); When the translation term of the affine map is lambda1: NewSphereMachine( "a=(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,a*b,b,b,b,b,b,b,b,b,b,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-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)", "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=(1,40)(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)", "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=(1,40)(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=(1,39)(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=(1,40)(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=(1,40)(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,a*b,b,b,b,b,b,b,b,b,b,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-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)", "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");