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 0/1, 0/3, 0/9, 0/18, 0/36, 1/12, 1/9, 1/6, 1/4, 1/3, 1/2, 2/4, 2/3, 1/1 2/1, 4/2, 5/2, 3/1, 9/3, 5/1, 7/1, 10/1, 11/1, 15/1, 21/1, 33/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-18.334699,-1.043558) ( -1.037736,-1.036364) ( -1.036145,-1.035294) ( -1.033793,-1.032886) ( -1.030570,-1.030040) ( -1.028571,-1.027027) ( -1.025832,-1.025453) ( -1.024043,-1.023580) ( -1.022901,-1.022556) ( -1.022472,-1.021978) ( -0.978022,-0.977528) ( -0.977444,-0.977099) ( -0.976420,-0.975957) ( -0.974547,-0.974168) ( -0.972973,-0.971429) ( -0.969960,-0.969430) ( -0.967114,-0.966207) ( -0.964706,-0.963855) ( -0.963636,-0.962264) ( -0.956243,-0.505376) ( -0.494624,-0.043757) ( -0.037736,-0.036364) ( -0.036145,-0.035294) ( -0.033793,-0.032886) ( -0.030570,-0.030040) ( -0.028571,-0.027027) ( -0.025832,-0.025453) ( -0.024043,-0.023580) ( -0.022901,-0.022556) ( -0.022472,-0.021978) ( 0.021978,0.022472 ) ( 0.022556,0.022901 ) ( 0.023580,0.024043 ) ( 0.025453,0.025832 ) ( 0.027027,0.028571 ) ( 0.030040,0.030570 ) ( 0.032886,0.033793 ) ( 0.035294,0.036145 ) ( 0.036364,0.037736 ) ( 0.043558,18.547639) The half-space computation does not determine rationality. EXCLUDED INTERVALS FOR JUST THE SUPPLEMENTAL HALF-SPACE COMPUTATION INTERVAL COMPUTED FOR HST OR EXTENDED HST ( -1.049261,-1.039024) -24/23 EXTENDED HST -> HST ( -1.045131,-1.033367) -27/26 EXTENDED HST -> HST ( -1.036364,-1.028881) -63/61 HST ( -1.032279,-1.032238) -32/31 EXTENDED HST ( -1.033309,-1.024698) -36/35 EXTENDED HST -> HST ( -1.024909,-1.024478) -83/81 HST ( -1.027233,-1.021721) -293/286 HST ( -1.024402,-1.024379) -42/41 EXTENDED HST ( -1.024686,-1.018344) -48/47 EXTENDED HST -> HST ( -1.020672,-1.015377) -56/55 HST ( -1.017036,-1.013582) -133/131 HST ( -1.015246,-1.015058) -67/66 HST ( -1.015600,-1.011619) -75/74 HST ( -1.012837,-1.010243) -175/173 HST ( -1.011533,-1.011456) -88/87 HST ( -1.011754,-1.008763) -99/98 HST ( -1.009920,-1.007399) -116/115 HST ( -1.008392,-1.006262) -137/136 HST ( -1.007136,-1.005326) -161/160 HST ( -1.005329,-1.005310) -189/188 HST ( -1.005698,-1.004927) -568/565 HST ( -1.005305,-1.005277) -190/189 HST ( -1.005173,-1.004681) -6935/6901 HST ( -1.004927,-1.004926) -204/203 EXTENDED HST ( -1.005338,-1.003986) -215/214 HST ( -1.004025,-0.996007) -1/1 EXTENDED HST ( -0.996317,-0.995081) -232/233 HST ( -0.995708,-0.994268) -198/199 HST ( -0.994967,-0.994931) -197/198 HST ( -0.994948,-0.993254) -169/170 HST ( -0.994113,-0.992143) -145/146 HST ( -0.993119,-0.990819) -124/125 HST ( -0.991955,-0.989270) -106/107 HST ( -0.990599,-0.988277) -94/95 HST ( -0.989366,-0.989357) -93/94 EXTENDED HST ( -0.989281,-0.989214) -92/93 HST ( -0.989217,-0.985632) -78/79 HST ( -0.987246,-0.987112) -77/78 HST ( -0.987016,-0.987010) -76/77 EXTENDED HST ( -0.986900,-0.986784) -75/76 HST ( -0.986704,-0.982298) -64/65 HST ( -0.984542,-0.979435) -54/55 HST ( -0.981541,-0.975467) -45/46 EXTENDED HST -> HST ( -0.975522,-0.975091) -79/81 HST ( -0.975956,-0.974202) -274/281 HST ( -0.975049,-0.974951) -39/40 EXTENDED HST ( -0.977094,-0.969601) -36/37 EXTENDED HST -> HST ( -0.969434,-0.968832) -63/65 HST ( -0.968847,-0.968803) -373/385 HST ( -0.968827,-0.968673) -31/32 EXTENDED HST ( -0.969725,-0.967532) -216/223 HST ( -0.968606,-0.967894) -61/63 HST ( -0.967762,-0.967721) -30/31 EXTENDED HST ( -0.969163,-0.965066) -59/61 HST ( -0.969824,-0.960050) -82/85 HST ( -0.960591,-0.951220) -22/23 EXTENDED HST -> HST ( -0.506864,-0.503860) -47/93 HST ( -0.504042,-0.495958) -1/2 EXTENDED HST ( -0.496140,-0.493136) -46/93 HST ( -0.048780,-0.039409) -1/23 EXTENDED HST -> HST ( -0.044623,-0.033746) -1/26 EXTENDED HST -> HST ( -0.036101,-0.029091) -2/61 HST ( -0.032279,-0.032238) -1/31 EXTENDED HST ( -0.033031,-0.024906) -1/35 EXTENDED HST -> HST ( -0.024909,-0.024478) -2/81 HST ( -0.027089,-0.021836) -7/286 HST ( -0.024402,-0.024379) -1/41 EXTENDED HST ( -0.024533,-0.018459) -1/46 EXTENDED HST -> HST ( -0.020565,-0.015458) -1/55 HST ( -0.017702,-0.013296) -1/65 HST ( -0.013385,-0.013282) -4/301 HST ( -0.013679,-0.012882) -10/753 HST ( -0.013275,-0.013273) -3/226 EXTENDED HST ( -0.013246,-0.013244) -2/151 EXTENDED HST ( -0.013216,-0.013100) -1/76 HST ( -0.012888,-0.012754) -1/78 HST ( -0.014368,-0.010783) -1/79 HST ( -0.010786,-0.010719) -1/93 HST ( -0.011876,-0.009547) -2/187 HST ( -0.010643,-0.010634) -1/94 EXTENDED HST ( -0.009550,-0.009498) -1/105 HST ( -0.010730,-0.008045) -1/106 HST ( -0.009181,-0.006881) -1/125 HST ( -0.007857,-0.005887) -1/146 HST ( -0.006746,-0.005052) -1/170 HST ( -0.005069,-0.005033) -1/198 HST ( -0.005732,-0.004292) -1/199 HST ( -0.004919,-0.003683) -1/233 HST ( -0.003993,0.004026 ) 0/1 EXTENDED HST ( 0.003826,0.005123 ) 1/223 HST ( 0.004488,0.006012 ) 1/190 HST ( 0.005277,0.005305 ) 1/189 HST ( 0.005310,0.005329 ) 1/188 HST ( 0.005326,0.007136 ) 1/160 HST ( 0.006262,0.008392 ) 1/136 HST ( 0.007399,0.009920 ) 1/115 HST ( 0.008763,0.011754 ) 1/97 HST ( 0.010354,0.013895 ) 1/83 HST ( 0.012112,0.016265 ) 1/70 HST ( 0.014432,0.014554 ) 1/69 HST ( 0.014634,0.014778 ) 1/68 HST ( 0.014921,0.014930 ) 1/67 EXTENDED HST ( 0.015058,0.015246 ) 1/66 HST ( 0.015377,0.020672 ) 1/55 HST ( 0.018344,0.024686 ) 1/46 EXTENDED HST -> HST ( 0.024478,0.024909 ) 2/81 HST ( 0.024001,0.025845 ) 7/281 HST ( 0.024951,0.025049 ) 1/40 EXTENDED HST ( 0.022730,0.030634 ) 1/37 EXTENDED HST -> HST ( 0.030566,0.031168 ) 2/65 HST ( 0.031153,0.031197 ) 12/385 HST ( 0.031173,0.031327 ) 1/32 EXTENDED HST ( 0.030206,0.032541 ) 7/223 HST ( 0.031394,0.032106 ) 2/63 HST ( 0.032238,0.032279 ) 1/31 EXTENDED HST ( 0.030702,0.035088 ) 2/61 HST ( 0.029872,0.040357 ) 2/57 HST ( 0.039024,0.049261 ) 1/23 EXTENDED HST -> HST -10.391602)(9.392578 infinity 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: 29284 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 |p'| <= |p| for every slope p/q with |p| <= 50 and |q| <= 50. 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=(1,35)(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^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c,c,c,c,c,c,c,c>(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=(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=(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,c^-1*b,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c,c,c,c,c,c,c,b^-1*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)", "a*b*c*d"); ****************************INTEGER OVERFLOW REPORT***************************** Imminent integer overflow occurred during the computation of a fixed point excluded interval about -134494/235663. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -134494/235663. Imminent integer overflow halted computation of the slope function at slope -2476647/1450457 during the modular group computation. This caused the modular group computation to abort.