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 0/40, 2/20, 2/10, 2/8, 2/5, 2/4, 4/5, 2/2, 2/1, 6/2, 4/1, 6/1, 14/2, 12/1 14/1, 18/1, 22/1, 28/1, 34/1, 36/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-infinity,infinity) The half-space computation determines rationality. The supplemental half-space computation is not needed. 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: 735 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=<1,1,d*a*d^-1,d*b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,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)", "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,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)", "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=<1,1,d*a*d^-1,d*b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*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)", "a*b*c*d"); When the translation term of the affine map is lambda1: NewSphereMachine( "a=<1,1,1,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c*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)", "b=<1,a,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,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>(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=<1,1,a,a^-1,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*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)", "a*b*c*d"); When the translation term of the affine map is lambda2: NewSphereMachine( "a=<1,1,d*b*c,d*a*d^-1,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*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>(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,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,d*a*d^-1,1,d*a,d*b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,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,a^-1,a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*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>(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,a,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,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,a,a^-1,a,a^-1,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,d*a,b*c,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");