These Thurston maps are NET maps for every choice of translation term. They are primitive and have degree 32. ALL THURSTON MULTIPLIERS c/d IN UNREDUCED FORM 0/32, 1/32, 1/16, 1/8, 1/4, 1/2, 3/4, 1/1, 5/4, 3/2, 2/1, 5/2, 3/1, 7/2 5/1, 6/1, 13/2, 7/1, 9/1, 10/1, 11/1, 13/1, 14/1, 15/1, 17/1, 18/1, 22/1 23/1, 26/1, 29/1, 30/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-infinity,-0.036023) (-0.035845,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 (-0.036098,-0.036003) -13/361 HST (-0.036008,-0.035992) -9/250 HST (-0.036007,-0.035976) -14/389 HST (-0.035980,-0.035973) -54/1501 HST (-0.035974,-0.035972) -194/5393 HST (-0.035972,-0.035970) -5/139 EXTENDED HST (-0.035973,-0.035966) -151/4198 HST (-0.035970,-0.035949) -21/584 HST (-0.035956,-0.035954) -16/445 HST (-0.035949,-0.035949) -82/2281 HST (-0.035950,-0.035948) -104/2893 HST (-0.035948,-0.035947) -11/306 EXTENDED HST (-0.035948,-0.035946) -149/4145 HST (-0.035947,-0.035946) -105/2921 HST (-0.035947,-0.035946) -94/2615 HST (-0.035946,-0.035946) -72/2003 HST (-0.035946,-0.035946) -61/1697 EXTENDED HST (-0.035946,-0.035946) -971/27013 HST (-0.035946,-0.035945) -50/1391 HST (-0.035945,-0.035945) -89/2476 HST (-0.035945,-0.035945) -362/10071 HST (-0.035945,-0.035945) -596/16581 HST (-0.035945,-0.035945) -39/1085 EXTENDED HST (-0.035945,-0.035944) -145/4034 HST (-0.035944,-0.035944) -67/1864 HST (-0.035944,-0.035943) -28/779 HST (-0.035944,-0.035942) -73/2031 HST (-0.035943,-0.035924) -6/167 HST (-0.035925,-0.035923) -49/1364 HST (-0.035923,-0.035921) -37/1030 HST (-0.035922,-0.035918) -25/696 HST (-0.035918,-0.035918) -63/1754 HST (-0.035918,-0.035917) -101/2812 HST (-0.035919,-0.035916) -177/4928 HST (-0.035917,-0.035917) -19/529 EXTENDED HST (-0.035916,-0.035915) -51/1420 HST (-0.035915,-0.035908) -13/362 HST (-0.035908,-0.035908) -53/1476 HST (-0.035908,-0.035907) -385/10722 HST (-0.035907,-0.035907) -93/2590 HST (-0.035907,-0.035906) -20/557 HST (-0.035907,-0.035905) -107/2980 HST (-0.035906,-0.035905) -87/2423 HST (-0.035906,-0.035903) -27/752 HST (-0.035905,-0.035901) -34/947 HST (-0.035903,-0.035898) -55/1532 HST (-0.035899,-0.035898) -369/10279 HST (-0.035898,-0.035898) -188/5237 HST (-0.035898,-0.035898) -244/6797 HST (-0.035899,-0.035897) -377/10502 HST (-0.035898,-0.035897) -7/195 EXTENDED HST (-0.035898,-0.035891) -71/1978 HST (-0.035895,-0.035885) -29/808 HST (-0.035890,-0.035878) -15/418 HST (-0.035880,-0.035875) -47/1310 HST (-0.035878,-0.035870) -8/223 HST (-0.035872,-0.035854) -17/474 HST (-0.035861,-0.035805) -9/251 HST The supplemental half-space computation shows that these NET maps are rational. SLOPE FUNCTION INFORMATION NUMBER OF FIXED POINTS FOUND: 1 EQUATOR? FIXED POINT c d 0 lambda1 lambda2 lambda1+lambda2 306/11 1 16 No No No No NUMBER OF EQUATORS FOUND: 0 0 0 0 The fixed point finder is unable to determine whether there are any more slope function fixed points. Number of excluded intervals computed by the fixed point finder: 3546 Here is their union. There are no more slope function fixed points whose negative reciprocals lie in any of the following intervals. EXCLUDED INTERVALS FOR THE FIXED POINT COMPUTATION (-infinity,-0.035946) (-0.035946,-0.035899) (-0.035899,infinity ) 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 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=(1,31)(2,30)(3,29)(4,28)(5,27)(6,26)(7,25)(8,24)(9,23)(10,22)(11,21)(12,20)(13,19)(14,18)(15,17)", "b=(1,31)(2,30)(3,29)(4,28)(5,27)(6,26)(7,25)(8,24)(9,23)(10,22)(11,21)(12,20)(13,19)(14,18)(15,17)", "c=(1,32)(2,31)(3,30)(4,29)(5,28)(6,27)(7,26)(8,25)(9,24)(10,23)(11,22)(12,21)(13,20)(14,19)(15,18)(16,17)", "d=(1,32)(2,31)(3,30)(4,29)(5,28)(6,27)(7,26)(8,25)(9,24)(10,23)(11,22)(12,21)(13,20)(14,19)(15,18)(16,17)", "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,c,c,c,c,c,c,c,c,c,c,c,c,c,c,c>(2,32)(3,31)(4,30)(5,29)(6,28)(7,27)(8,26)(9,25)(10,24)(11,23)(12,22)(13,21)(14,20)(15,19)(16,18)", "b=<1,d*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>(2,32)(3,31)(4,30)(5,29)(6,28)(7,27)(8,26)(9,25)(10,24)(11,23)(12,22)(13,21)(14,20)(15,19)(16,18)", "c=(1,32)(2,31)(3,30)(4,29)(5,28)(6,27)(7,26)(8,25)(9,24)(10,23)(11,22)(12,21)(13,20)(14,19)(15,18)(16,17)", "d=(1,32)(2,31)(3,30)(4,29)(5,28)(6,27)(7,26)(8,25)(9,24)(10,23)(11,22)(12,21)(13,20)(14,19)(15,18)(16,17)", "a*b*c*d"); When the translation term of the affine map is lambda2: NewSphereMachine( "a=(1,32)(2,31)(3,30)(4,29)(5,28)(6,27)(7,26)(8,25)(9,24)(10,23)(11,22)(12,21)(13,20)(14,19)(15,18)(16,17)", "b=(1,32)(2,31)(3,30)(4,29)(5,28)(6,27)(7,26)(8,25)(9,24)(10,23)(11,22)(12,21)(13,20)(14,19)(15,18)(16,17)", "c=(1,31)(2,30)(3,29)(4,28)(5,27)(6,26)(7,25)(8,24)(9,23)(10,22)(11,21)(12,20)(13,19)(14,18)(15,17)", "d=(1,31)(2,30)(3,29)(4,28)(5,27)(6,26)(7,25)(8,24)(9,23)(10,22)(11,21)(12,20)(13,19)(14,18)(15,17)", "a*b*c*d"); When the translation term of the affine map is lambda1+lambda2: NewSphereMachine( "a=(1,32)(2,31)(3,30)(4,29)(5,28)(6,27)(7,26)(8,25)(9,24)(10,23)(11,22)(12,21)(13,20)(14,19)(15,18)(16,17)", "b=(1,32)(2,31)(3,30)(4,29)(5,28)(6,27)(7,26)(8,25)(9,24)(10,23)(11,22)(12,21)(13,20)(14,19)(15,18)(16,17)", "c=<1,d*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>(2,32)(3,31)(4,30)(5,29)(6,28)(7,27)(8,26)(9,25)(10,24)(11,23)(12,22)(13,21)(14,20)(15,19)(16,18)", "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^-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*a>(2,32)(3,31)(4,30)(5,29)(6,28)(7,27)(8,26)(9,25)(10,24)(11,23)(12,22)(13,21)(14,20)(15,19)(16,18)", "a*b*c*d"); ****************************INTEGER OVERFLOW REPORT***************************** Imminent integer overflow halted evaluation of the slope function at slope 2182772/78463 during the search for all slope function fixed points. Imminent integer overflow halted evaluation of the slope function at slope 2714411/97444 during the search for all slope function fixed points. Imminent integer overflow halted evaluation of the slope function at slope 2236233/80278 during the search for all slope function fixed points. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -40011/1114589. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -40011/1114589. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -64189/1788119. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -64189/1788119. Imminent integer overflow halted evaluation of the slope function at slope 2071603/74364 during the search for all slope function fixed points. Imminent integer overflow caused the modular group computation to abort.