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, 0/10, 0/40, 1/40, 1/20, 1/10, 1/8, 1/5, 1/4, 2/8, 1/2, 2/4, 3/5 4/5, 1/1, 5/5, 3/2, 6/4, 3/1, 7/2, 4/1, 8/2, 9/2, 7/1, 16/2, 9/1, 11/1, 12/1 13/1, 17/1, 19/1, 28/1, 31/1, 36/1, 37/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-58.202646,58.202646) The half-space computation does not determine rationality. EXCLUDED INTERVALS FOR JUST THE SUPPLEMENTAL HALF-SPACE COMPUTATION INTERVAL COMPUTED FOR HST OR EXTENDED HST -6.324219)(6.325195 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: 4706 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. FUNDAMENTAL GROUP WREATH RECURSIONS When the translation term of the affine map is 0: NewSphereMachine( "a=<1,b*c,d*a*c,c^-1*b*c,d*a*c,c^-1*b*c,d*a*c,c^-1*b*c,d*a*c,c^-1*b*c,d*a*c,c^-1*b*c,d*a*c,c^-1*b*c,d*a*c,c^-1*b*c,d*a*c,c^-1*b*c,d*a*c,c^-1*b*c,d*a*c,c^-1*b*c,d*a*c,c^-1*b*c,d*a*c,c^-1*b*c,d*a*c,c^-1*b*c,d*a*c,c^-1*b*c,d*a*c,c^-1*b*c,d*a*c,c^-1*b*c,d*a*c,c^-1*b*c,d*a*c,c^-1*b*c,d*a*c,c^-1*b*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)", "b=<1,1,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>(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>(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=(1,2)(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)", "a*b*c*d"); When the translation term of the affine map is lambda1: NewSphereMachine( "a=<1,a^-1*c^-1,b^-1,b,b^-1,b,b^-1,b,b^-1,b,b^-1,b,b^-1,b,b^-1,b,b^-1,b,b^-1,b,b^-1,b,b^-1,b,b^-1,b,b^-1,b,b^-1,b,b^-1,b,b^-1,b,b^-1,b,b^-1,b,b^-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,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,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=(1,2)(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=(1,2)(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)", "a*b*c*d"); When the translation term of the affine map is lambda2: NewSphereMachine( "a=<1,a,c^-1*b*c,d*a*c,c^-1*b*c,d*a*c,c^-1*b*c,d*a*c,c^-1*b*c,d*a*c,c^-1*b*c,d*a*c,c^-1*b*c,d*a*c,c^-1*b*c,d*a*c,c^-1*b*c,d*a*c,c^-1*b*c,d*a*c,c^-1*b*c,d*a*c,c^-1*b*c,d*a*c,c^-1*b*c,d*a*c,c^-1*b*c,d*a*c,c^-1*b*c,d*a*c,c^-1*b*c,d*a*c,c^-1*b*c,d*a*c,c^-1*b*c,d*a*c,c^-1*b*c,d*a*c,c^-1*b*c,d*a*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)", "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>(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,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>(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*c,a^-1,d*a*c,c^-1*b*c,d*a*c,c^-1*b*c,d*a*c,c^-1*b*c,d*a*c,c^-1*b*c,d*a*c,c^-1*b*c,d*a*c,c^-1*b*c,d*a*c,c^-1*b*c,d*a*c,c^-1*b*c,d*a*c,c^-1*b*c,d*a*c,c^-1*b*c,d*a*c,c^-1*b*c,d*a*c,c^-1*b*c,d*a*c,c^-1*b*c,d*a*c,c^-1*b*c,d*a*c,c^-1*b*c,d*a*c,c^-1*b*c,d*a*c,c^-1*b*c,d*a*c,c^-1*b*c,c^-1*b*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)", "a*b*c*d"); When the translation term of the affine map is lambda1+lambda2: NewSphereMachine( "a=<1,1,b,b^-1,b,b^-1,b,b^-1,b,b^-1,b,b^-1,b,b^-1,b,b^-1,b,b^-1,b,b^-1,b,b^-1,b,b^-1,b,b^-1,b,b^-1,b,b^-1,b,b^-1,b,b^-1,b,b^-1,b,b^-1,b,b^-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)", "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,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,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)", "d=<1,d*a,a^-1,b^-1,b,b^-1,b,b^-1,b,b^-1,b,b^-1,b,b^-1,b,b^-1,b,b^-1,b,b^-1,b,b^-1,b,b^-1,b,b^-1,b,b^-1,b,b^-1,b,b^-1,b,b^-1,b,b^-1,b,b^-1,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)", "a*b*c*d");