These Thurston maps are NET maps for every choice of translation term. They are primitive and have degree 36. ALL THURSTON MULTIPLIERS c/d IN UNREDUCED FORM 0/36, 1/36, 1/18, 1/12, 1/9, 1/6, 2/12, 1/4, 1/3, 3/9, 1/2, 2/4, 5/6, 1/1 4/4, 5/4, 5/3, 7/4, 8/4, 7/3, 5/2, 7/2, 11/3, 5/1, 11/2, 13/2, 7/1, 17/2 11/1, 13/1, 17/1, 19/1, 23/1, 25/1, 29/1, 31/1, 35/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-infinity,0.000000) ( 0.000000,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 (-0.005926,0.007314) 0/1 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: 428 NONTRIVIAL CYCLES 2/1 -> -36/1 -> -2/1 -> 10/1 -> -4/1 -> 6/1 -> -8/1 -> 2/1 18/5 -> -68/5 -> 34/5 -> -36/5 -> 18/5 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 either one of the above cycles or 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)", "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>(1,2)(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=<1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,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)", "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)(34,36)", "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)", "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)", "c=<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>(1,2)(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=(1,4)(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)", "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)", "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,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)", "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>(1,2)(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=(1,4)(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)", "a*b*c*d"); When the translation term of the affine map is lambda1+lambda2: NewSphereMachine( "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)", "b=<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>(1,2)(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=(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)", "d=<1,d*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,c^-1,b*c,c>(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)(34,36)", "a*b*c*d"); ****************************INTEGER OVERFLOW REPORT***************************** Imminent integer overflow caused the modular group computation to abort.