These Thurston maps are NET maps for every choice of translation term. They are primitive and have degree 37. ALL THURSTON MULTIPLIERS c/d IN UNREDUCED FORM 0/1, 1/37, 1/1, 2/1, 3/1, 4/1, 5/1, 7/1, 8/1, 9/1, 11/1, 13/1, 14/1, 16/1 18/1, 19/1, 21/1, 25/1, 29/1, 31/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-58.640427,58.640427) The half-space computation does not determine rationality. EXCLUDED INTERVALS FOR JUST THE SUPPLEMENTAL HALF-SPACE COMPUTATION INTERVAL COMPUTED FOR HST OR EXTENDED HST -6.082031)(6.083008 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 because every loop multiplier of the mod 2 slope correspondence graph is at least 1 and the map is rational. 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,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,c,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)", "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>(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)", "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,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)", "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)", "a*b*c*d"); When the translation term of the affine map is lambda1: NewSphereMachine( "a=<1,a^-1,d*a,c,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,c,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)", "b=<1,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>(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)", "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)", "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)", "a*b*c*d"); When the translation term of the affine map is lambda2: NewSphereMachine( "a=<1,a,c,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-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)", "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,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)", "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>(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)", "d=<1,a*b,a^-1,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,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)", "a*b*c*d"); When the translation term of the affine map is lambda1+lambda2: NewSphereMachine( "a=<1,1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,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)", "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)", "c=<1,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>(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)", "d=<1,c^-1,c*d,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,c,c^-1,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)", "a*b*c*d");