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 0/12, 0/36, 1/36, 1/18, 1/12, 1/9, 1/6, 2/9, 1/4, 1/3, 1/2, 2/4, 3/6, 2/3 3/4, 1/1, 3/3, 4/4, 3/2, 6/4, 5/3, 2/1, 5/2, 3/1, 9/3, 10/3, 7/2, 5/1, 7/1 15/2, 10/1, 11/1, 13/1, 14/1, 15/1, 17/1, 21/1, 22/1, 26/1, 33/1, 34/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-infinity,-0.031417) (-0.031347,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 (-0.031419,-0.031410) -6/191 HST (-0.031425,-0.031402) -43/1369 HST -0.031388)(-0.031356 -13/414 HST (-0.031390,-0.031390) -7/223 EXTENDED HST (-0.031414,-0.031382) -29/924 HST (-0.031385,-0.031379) -15/478 HST (-0.031382,-0.031378) -38/1211 HST (-0.031378,-0.031378) -23/733 EXTENDED HST (-0.031378,-0.031375) -31/988 HST (-0.031375,-0.031363) -8/255 HST (-0.031368,-0.031332) -35/1116 HST (-0.031359,-0.031359) -9/287 EXTENDED HST The supplemental half-space computation shows that these NET maps are rational. SLOPE FUNCTION INFORMATION There are no slope function fixed points p/q with |p| <= 50 and |q| <= 50. The fixed point finder is unable to determine whether there are any slope function fixed points. Number of excluded intervals computed by the fixed point finder: 1317 Here is their union. There are no slope function fixed points whose negative reciprocals lie in any of the following intervals. EXCLUDED INTERVALS FOR THE FIXED POINT COMPUTATION (-infinity,-0.031357) (-0.031357,infinity ) NONTRIVIAL CYCLES 32/1 -> 255/8 -> 478/15 -> 988/31 -> 32/1 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. FUNDAMENTAL GROUP WREATH RECURSIONS When the translation term of the affine map is 0: NewSphereMachine( "a=(1,35)(2,34)(3,33)(4,32)(5,31)(6,30)(7,29)(8,28)(9,27)(10,26)(11,25)(12,24)(13,23)(14,22)(15,21)(16,20)(17,19)", "b=(1,35)(2,34)(3,33)(4,32)(5,31)(6,30)(7,29)(8,28)(9,27)(10,26)(11,25)(12,24)(13,23)(14,22)(15,21)(16,20)(17,19)", "c=(1,36)(2,35)(3,34)(4,33)(5,32)(6,31)(7,30)(8,29)(9,28)(10,27)(11,26)(12,25)(13,24)(14,23)(15,22)(16,21)(17,20)(18,19)", "d=(1,36)(2,35)(3,34)(4,33)(5,32)(6,31)(7,30)(8,29)(9,28)(10,27)(11,26)(12,25)(13,24)(14,23)(15,22)(16,21)(17,20)(18,19)", "a*b*c*d"); When the translation term of the affine map is lambda1: NewSphereMachine( "a=<1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c>(2,36)(3,35)(4,34)(5,33)(6,32)(7,31)(8,30)(9,29)(10,28)(11,27)(12,26)(13,25)(14,24)(15,23)(16,22)(17,21)(18,20)", "b=<1,d*b,b,b,b,b,b,b,b,b,b,b,b,b,b,b,b,b,b,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1>(2,36)(3,35)(4,34)(5,33)(6,32)(7,31)(8,30)(9,29)(10,28)(11,27)(12,26)(13,25)(14,24)(15,23)(16,22)(17,21)(18,20)", "c=(1,36)(2,35)(3,34)(4,33)(5,32)(6,31)(7,30)(8,29)(9,28)(10,27)(11,26)(12,25)(13,24)(14,23)(15,22)(16,21)(17,20)(18,19)", "d=(1,36)(2,35)(3,34)(4,33)(5,32)(6,31)(7,30)(8,29)(9,28)(10,27)(11,26)(12,25)(13,24)(14,23)(15,22)(16,21)(17,20)(18,19)", "a*b*c*d"); When the translation term of the affine map is lambda2: NewSphereMachine( "a=(1,36)(2,35)(3,34)(4,33)(5,32)(6,31)(7,30)(8,29)(9,28)(10,27)(11,26)(12,25)(13,24)(14,23)(15,22)(16,21)(17,20)(18,19)", "b=(1,36)(2,35)(3,34)(4,33)(5,32)(6,31)(7,30)(8,29)(9,28)(10,27)(11,26)(12,25)(13,24)(14,23)(15,22)(16,21)(17,20)(18,19)", "c=(1,35)(2,34)(3,33)(4,32)(5,31)(6,30)(7,29)(8,28)(9,27)(10,26)(11,25)(12,24)(13,23)(14,22)(15,21)(16,20)(17,19)", "d=(1,35)(2,34)(3,33)(4,32)(5,31)(6,30)(7,29)(8,28)(9,27)(10,26)(11,25)(12,24)(13,23)(14,22)(15,21)(16,20)(17,19)", "a*b*c*d"); When the translation term of the affine map is lambda1+lambda2: NewSphereMachine( "a=(1,36)(2,35)(3,34)(4,33)(5,32)(6,31)(7,30)(8,29)(9,28)(10,27)(11,26)(12,25)(13,24)(14,23)(15,22)(16,21)(17,20)(18,19)", "b=(1,36)(2,35)(3,34)(4,33)(5,32)(6,31)(7,30)(8,29)(9,28)(10,27)(11,26)(12,25)(13,24)(14,23)(15,22)(16,21)(17,20)(18,19)", "c=<1,d*b,b,b,b,b,b,b,b,b,b,b,b,b,b,b,b,b,b,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1>(2,36)(3,35)(4,34)(5,33)(6,32)(7,31)(8,30)(9,29)(10,28)(11,27)(12,26)(13,25)(14,24)(15,23)(16,22)(17,21)(18,20)", "d=<1,a^-1*b,b*c*b,b*c*b,b*c*b,b*c*b,b*c*b,b*c*b,b*c*b,b*c*b,b*c*b,b*c*b,b*c*b,b*c*b,b*c*b,b*c*b,b*c*b,b*c*b,b^-1*c*b,b^-1*d*a,b^-1*d*a,b^-1*d*a,b^-1*d*a,b^-1*d*a,b^-1*d*a,b^-1*d*a,b^-1*d*a,b^-1*d*a,b^-1*d*a,b^-1*d*a,b^-1*d*a,b^-1*d*a,b^-1*d*a,b^-1*d*a,b^-1*d*a,b^-1*a>(2,36)(3,35)(4,34)(5,33)(6,32)(7,31)(8,30)(9,29)(10,28)(11,27)(12,26)(13,25)(14,24)(15,23)(16,22)(17,21)(18,20)", "a*b*c*d"); ****************************INTEGER OVERFLOW REPORT***************************** Imminent integer overflow occurred during the computation of a fixed point excluded interval about -24489/780659. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -24489/780659. Imminent integer overflow halted evaluation of the slope function at slope 2409622/75589 during the search for all slope function fixed points. Imminent integer overflow halted evaluation of the slope function at slope 1847551/57934 during the search for all slope function fixed points. Imminent integer overflow caused the modular group computation to abort.