These Thurston maps are NET maps for every choice of translation term. They are primitive and have degree 39. ALL THURSTON MULTIPLIERS c/d IN UNREDUCED FORM 0/39, 2/13, 2/3, 4/3, 2/1, 6/3, 8/3, 4/1, 8/1, 10/1, 14/1, 16/1, 34/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-infinity,-0.012403) ( 0.012155,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 (-0.016978,-0.007412) -1/81 HST (-0.010057,0.010057 ) 0/1 EXTENDED HST ( 0.007323,0.016774 ) 1/83 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: 5540 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=(2,3)(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=<1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1>(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)", "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>(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)", "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)", "b=(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=<1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1>(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)", "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)(37,39)", "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)", "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>(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=<1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1>(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)", "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)(37,39)", "a*b*c*d"); When the translation term of the affine map is lambda1+lambda2: NewSphereMachine( "a=<1,a,a^-1,d*a,b*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>(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=<1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1>(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)", "c=(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,a,1,c^-1,a^-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>(1,3)(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)", "a*b*c*d");