These Thurston maps are NET maps for every choice of translation term. They are primitive and have degree 39. ALL THURSTON MULTIPLIERS c/d IN UNREDUCED FORM 0/13, 0/39, 2/3, 4/3, 2/1, 6/3, 4/1, 6/1, 8/1, 10/1, 14/1, 32/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-infinity,-0.067492) (-0.051282,-0.046512) (-0.038192,-0.035950) (-0.025916,-0.024146) ( 0.025372,0.027333 ) ( 0.038735,0.041351 ) ( 0.044561,0.077888 ) ( 0.078024,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 (-0.074850,-0.050972) -1/15 EXTENDED HST -> HST (-0.056125,-0.032110) -1/22 EXTENDED HST -> HST (-0.040601,-0.023229) -1/32 EXTENDED HST -> HST (-0.028695,-0.016417) -1/44 EXTENDED HST -> HST (-0.020630,-0.011803) -1/61 HST (-0.014619,-0.009134) -1/85 HST (-0.011636,-0.006657) -1/110 HST (-0.008109,-0.005066) -1/151 HST (-0.006007,0.006080 ) 0/1 EXTENDED HST ( 0.004447,0.007773 ) 1/162 HST ( 0.006200,0.012874 ) 1/104 HST ( 0.009662,0.015464 ) 1/79 HST ( 0.012753,0.013230 ) 1/77 HST ( 0.013154,0.022991 ) 1/55 HST ( 0.018439,0.018879 ) 1/53 HST ( 0.018942,0.030319 ) 1/40 EXTENDED HST -> HST ( 0.024205,0.050263 ) 1/26 EXTENDED HST -> HST ( 0.074066,0.082032 ) 6/77 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. Number of excluded intervals computed by the fixed point finder: 31435 The union of the excluded intervals computed by the fixed point finder became a union of 10,000 disjoint intervals: the search for all slope function fixed points aborted. 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,d*a*d^-1,1,d*a,d*b*c,d*a*c,b*c,1,c^-1*b*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>(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)(36,37)(38,39)", "b=<1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1>(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)(37,38)", "c=<1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1>(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)(36,37)(38,39)", "d=<1,d*a*d^-1,1,d*a,d*b*c,d*a*c,b*c,1,c^-1*b*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>(1,3)(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)(34,37)(36,39)", "a*b*c*d"); When the translation term of the affine map is lambda1: NewSphereMachine( "a=<1,1,a,a^-1,d*a,b*c,b^-1,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>(1,2)(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)(37,38)", "b=<1,a,1,1,d,1,c,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>(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)(36,37)(38,39)", "c=<1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1>(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)(37,38)", "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)(35,38)(37,39)", "a*b*c*d"); When the translation term of the affine map is lambda2: NewSphereMachine( "a=<1,1,d*a*d^-1,d*b*c,d*a,b*c,d*a*c,c^-1*b*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>(1,2)(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)(37,38)", "b=<1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1>(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)(36,37)(38,39)", "c=<1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1>(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)(37,38)", "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)(35,38)(37,39)", "a*b*c*d"); When the translation term of the affine map is lambda1+lambda2: NewSphereMachine( "a=<1,a,a^-1,a,a^-1,d*a,b*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>(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)(36,37)(38,39)", "b=<1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1>(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)(37,38)", "c=<1,a,1,1,d,1,c,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>(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)(36,37)(38,39)", "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)(34,37)(36,39)", "a*b*c*d"); ****************************INTEGER OVERFLOW REPORT***************************** Imminent integer overflow occurred during the computation of a fixed point excluded interval about -1/2646. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -1/4307. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -1/4346. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -1/4385. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -1/4844. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -2/10483. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -1/5328. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -1/5373. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -1/5588. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -1/5705. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -1/7167. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -2/14461. Imminent integer overflow occurred during the computation of a fixed point excluded interval about -1/7401. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 1/2307. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 1/2683. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 1/4188. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 1/4227. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 1/4266. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 1/4305. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 1/4344. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 1/4383. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 1/4842. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 1/5625. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 1/6411. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 1/6957. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 1/7113. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 1/7204. Imminent integer overflow occurred during the computation of a fixed point excluded interval about 1/7269. Imminent integer overflow halted computation of the slope function at slope -3378081/8708773 during the modular group computation. This caused the modular group computation to abort.