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 0/37, 1/37, 1/1, 2/1, 3/1, 4/1, 5/1, 6/1, 7/1, 8/1, 9/1, 10/1, 11/1, 12/1 13/1, 14/1, 16/1, 17/1, 18/1, 23/1, 27/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-infinity,-1.000000) (-0.983177,-0.600000) (-0.600000,-0.559667) (-0.559398,-0.558260) (-0.553091,-0.552180) (-0.550836,-0.534377) (-0.531574,-0.530932) (-0.528034,-0.527526) (-0.525207,-0.524796) (-0.522898,-0.522559) (-0.520977,-0.520692) (-0.517241,-0.511111) (-0.488949,-0.482611) (-0.482101,-0.470890) (-0.469068,-0.468426) (-0.466279,-0.339048) (-0.333333,-0.016823) ( 0.016603,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 (-1.004483,-0.995557) -1/1 EXTENDED HST (-0.995976,-0.994411) -208/209 HST (-0.995198,-0.993308) -174/175 HST (-0.994277,-0.992025) -145/146 HST (-0.993132,-0.990481) -122/123 HST (-0.991808,-0.988584) -102/103 HST (-0.990246,-0.986512) -86/87 HST (-0.988394,-0.983828) -71/72 HST (-0.985997,-0.980699) -59/60 HST (-0.600178,-0.599823) -3/5 EXTENDED HST (-0.561003,-0.558021) -47/84 HST (-0.559353,-0.555946) -29/52 HST (-0.556004,-0.555883) -159/286 HST (-0.555933,-0.555831) -189/340 HST (-0.555868,-0.555782) -229/412 HST (-0.555813,-0.555740) -274/493 HST (-0.555768,-0.555708) -339/610 HST (-0.555731,-0.555682) -409/736 HST (-0.555740,-0.555618) -494/889 HST (-0.555628,-0.555608) -984/1771 HST (-0.555610,-0.555501) -5/9 EXTENDED HST (-0.555741,-0.555152) -596/1073 HST (-0.555452,-0.555413) -501/902 HST (-0.555432,-0.555187) -256/461 HST (-0.555313,-0.555213) -211/380 HST (-0.555257,-0.555132) -171/308 HST (-0.555194,-0.555041) -146/263 HST (-0.555129,-0.554963) -121/218 HST (-0.555044,-0.554846) -101/182 HST (-0.554918,-0.554671) -86/155 HST (-0.554822,-0.551274) -26/47 EXTENDED HST -> HST (-0.551951,-0.549731) -27/49 EXTENDED HST -> HST (-0.535692,-0.532465) -39/73 HST (-0.533353,-0.533314) -8/15 EXTENDED HST (-0.536545,-0.527750) -197/370 HST (-0.532430,-0.532088) -33/62 HST (-0.531921,-0.531909) -25/47 EXTENDED HST (-0.531443,-0.523699) -29/55 HST (-0.526328,-0.526303) -10/19 EXTENDED HST (-0.524788,-0.521676) -34/65 HST (-0.522260,-0.520843) -121/232 HST (-0.521543,-0.521467) -97/186 HST (-0.521479,-0.521378) -73/140 HST (-0.521369,-0.521366) -61/117 EXTENDED HST (-0.521351,-0.521202) -49/94 HST (-0.521129,-0.521124) -37/71 EXTENDED HST (-0.521574,-0.516703) -13/25 EXTENDED HST -> HST (-0.517271,-0.517211) -15/29 EXTENDED HST (-0.512298,-0.508587) -23/45 EXTENDED HST -> HST (-0.508590,-0.508578) -237/466 HST (-0.508579,-0.508574) -504/991 HST (-0.508647,-0.508501) -1216/2391 HST (-0.508572,-0.508571) -89/175 EXTENDED HST (-0.508748,-0.508250) -329/647 HST (-0.508476,-0.508473) -30/59 EXTENDED HST (-0.508410,-0.507827) -31/61 HST (-0.507833,-0.507792) -65/128 HST (-0.508253,-0.507272) -98/193 HST (-0.507693,-0.507691) -33/65 EXTENDED HST (-0.507514,-0.507022) -314/619 HST (-0.507247,-0.507245) -35/69 EXTENDED HST (-0.509934,-0.503448) -37/73 HST (-0.503979,-0.502868) -73/145 HST (-0.503356,-0.496689) -1/2 EXTENDED HST (-0.498282,-0.495017) -73/147 HST (-0.496599,-0.489933) -38/77 HST (-0.493472,-0.490903) -32/65 HST (-0.492216,-0.489284) -27/55 HST (-0.490780,-0.486360) -23/47 EXTENDED HST -> HST (-0.483615,-0.481337) -41/85 HST (-0.482247,-0.482037) -27/56 HST (-0.470920,-0.470827) -97/206 HST (-0.470838,-0.470768) -121/257 HST (-0.470788,-0.470732) -161/342 HST (-0.471570,-0.469915) -193/410 HST (-0.470604,-0.470573) -8/17 EXTENDED HST (-0.471073,-0.468968) -39/83 HST (-0.469847,-0.469545) -31/66 HST (-0.469393,-0.469382) -23/49 EXTENDED HST (-0.469752,-0.465815) -22/47 EXTENDED HST -> HST (-0.466686,-0.466647) -7/15 EXTENDED HST (-0.339369,-0.337999) -20/59 HST (-0.338925,-0.337105) -25/74 HST (-0.337629,-0.336308) -30/89 HST (-0.336698,-0.335721) -38/113 HST (-0.336119,-0.335314) -47/140 HST (-0.335625,-0.334965) -57/170 HST (-0.335206,-0.334694) -69/206 HST (-0.334896,-0.334458) -82/245 HST (-0.334643,-0.334239) -100/299 HST (-0.334370,-0.334079) -124/371 HST (-0.334191,-0.333950) -150/449 HST (-0.334052,-0.333846) -181/542 HST (-0.333926,-0.333758) -218/653 HST (-0.333830,-0.332838) -1/3 EXTENDED HST (-0.019196,-0.014081) -1/60 HST (-0.016099,-0.011659) -1/72 HST (-0.013437,-0.009791) -1/86 HST (-0.011161,-0.008060) -1/103 HST (-0.009241,-0.006632) -1/125 HST (-0.007628,-0.005521) -1/151 HST (-0.006386,-0.004600) -1/182 HST (-0.005341,-0.003833) -1/218 HST (-0.004404,0.004483 ) 0/1 EXTENDED HST ( 0.003935,0.005501 ) 1/212 HST ( 0.004730,0.006641 ) 1/176 HST ( 0.005710,0.007993 ) 1/147 HST ( 0.006831,0.009570 ) 1/123 HST ( 0.008140,0.011490 ) 1/103 HST ( 0.009716,0.013540 ) 1/87 HST ( 0.011553,0.016246 ) 1/72 HST ( 0.013927,0.019407 ) 1/61 HST The supplemental half-space computation shows that these NET maps are rational. SLOPE FUNCTION INFORMATION NUMBER OF FIXED POINTS: 2 EQUATOR? FIXED POINT c d 0 lambda1 lambda2 lambda1+lambda2 2/1 1 37 No No Yes Yes 4/1 1 37 No No Yes Yes NUMBER OF EQUATORS: 0 0 2 2 There are no more slope function fixed points. Number of excluded intervals computed by the fixed point finder: 17746 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. 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=(1,36)(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=(1,37)(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=(1,37)(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"); When the translation term of the affine map is lambda1: NewSphereMachine( "a=(2,37)(3,36)(4,35)(5,34)(6,33)(7,32)(8,31)(9,30)(10,29)(11,28)(12,27)(13,26)(14,25)(15,24)(16,23)(17,22)(18,21)(19,20)", "b=<1,b,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c,c,c,c,c,c,c,c,b^-1*c>(2,37)(3,36)(4,35)(5,34)(6,33)(7,32)(8,31)(9,30)(10,29)(11,28)(12,27)(13,26)(14,25)(15,24)(16,23)(17,22)(18,21)(19,20)", "c=(1,37)(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=(1,37)(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"); When the translation term of the affine map is lambda2: NewSphereMachine( "a=(1,37)(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=(1,37)(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 lambda1+lambda2: NewSphereMachine( "a=(1,37)(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=(1,37)(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,b,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c,c,c,c,c,c,c,c,b^-1*c>(2,37)(3,36)(4,35)(5,34)(6,33)(7,32)(8,31)(9,30)(10,29)(11,28)(12,27)(13,26)(14,25)(15,24)(16,23)(17,22)(18,21)(19,20)", "d=(2,37)(3,36)(4,35)(5,34)(6,33)(7,32)(8,31)(9,30)(10,29)(11,28)(12,27)(13,26)(14,25)(15,24)(16,23)(17,22)(18,21)(19,20)", "a*b*c*d");