These Thurston maps are NET maps for every choice of translation term. They are primitive and have degree 17. PURE MODULAR GROUP HURWITZ EQUIVALENCE CLASSES FOR TRANSLATIONS {0} {lambda1} {lambda2} {lambda1+lambda2} These pure modular group Hurwitz classes each contain only finitely many Thurston equivalence classes. However, this modular group Hurwitz class contains infinitely many Thurston equivalence classes. The number of pure modular group Hurwitz classes in this modular group Hurwitz class is 24. ALL THURSTON MULTIPLIERS c/d IN UNREDUCED FORM 0/1, 0/17, 1/17, 1/1, 2/1, 3/1, 4/1, 5/1, 6/1, 7/1, 9/1, 11/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-infinity,-0.088948) (-0.086312,-0.085124) (-0.081616,-0.080553) (-0.078385,-0.075514) (-0.073606,-0.072740) (-0.070163,-0.069376) (-0.067762,-0.065606) (-0.064161,-0.063502) (-0.061529,-0.060923) (-0.059675,-0.057996) (-0.053312,-0.051968) (-0.048175,-0.047075) (-0.043942,-0.043025) (-0.040392,-0.039616) (-0.037373,-0.036707) (-0.034774,-0.034197) (-0.032512,-0.032008) (-0.030527,-0.030082) (-0.028771,-0.028375) (-0.027205,-0.026851) (-0.025801,-0.025483) (-0.024535,-0.024247) (-0.023388,-0.023125) (-0.022343,-0.022103) (-0.021387,-0.021167) (-0.020510,-0.020308) ( 0.020308,0.020510 ) ( 0.021167,0.021387 ) ( 0.022103,0.022343 ) ( 0.023125,0.023388 ) ( 0.024247,0.024535 ) ( 0.025483,0.025801 ) ( 0.026851,0.027205 ) ( 0.028375,0.028771 ) ( 0.030082,0.030527 ) ( 0.032008,0.032512 ) ( 0.034197,0.034774 ) ( 0.036707,0.037373 ) ( 0.039616,0.040392 ) ( 0.043025,0.043942 ) ( 0.047075,0.048175 ) ( 0.051968,0.053312 ) ( 0.057996,0.059675 ) ( 0.060923,0.061529 ) ( 0.063502,0.064161 ) ( 0.065606,0.067762 ) ( 0.069376,0.070163 ) ( 0.072740,0.073606 ) ( 0.075514,0.078385 ) ( 0.080553,0.081616 ) ( 0.085124,0.086312 ) ( 0.088948,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 (-0.094458,-0.082721) -4/45 EXTENDED HST -> HST (-0.088272,-0.088198) -3/34 EXTENDED HST (-0.087010,-0.086903) -2/23 EXTENDED HST (-0.088859,-0.074909) -4/49 EXTENDED HST -> HST (-0.075221,-0.074561) -20/267 HST (-0.074898,-0.074358) -5/67 HST (-0.076951,-0.071613) -11/148 HST (-0.074113,-0.074035) -2/27 EXTENDED HST (-0.072672,-0.070534) -28/391 HST (-0.071501,-0.071356) -1/14 EXTENDED HST (-0.076471,-0.064249) -4/57 HST (-0.064363,-0.064078) -7/109 HST (-0.069219,-0.057327) -4/63 HST (-0.062556,-0.062444) -1/16 EXTENDED HST (-0.063406,-0.051225) -9/157 HST (-0.057166,-0.057120) -2/35 EXTENDED HST (-0.055600,-0.055512) -1/18 EXTENDED HST (-0.054281,-0.048082) -15/293 HST (-0.051186,-0.051005) -7/137 HST (-0.051057,-0.050639) -3/59 HST (-0.050036,-0.049964) -1/20 EXTENDED HST (-0.050154,-0.043796) -4/85 HST (-0.046885,-0.046865) -3/64 EXTENDED HST (-0.046527,-0.046496) -2/43 EXTENDED HST (-0.045484,-0.045425) -1/22 EXTENDED HST (-0.045852,-0.040028) -4/93 HST (-0.042866,-0.042848) -3/70 EXTENDED HST (-0.042566,-0.042540) -2/47 EXTENDED HST (-0.041691,-0.041642) -1/24 EXTENDED HST (-0.042231,-0.036858) -4/101 HST (-0.039481,-0.039466) -3/76 EXTENDED HST (-0.039227,-0.039205) -2/51 EXTENDED HST (-0.038483,-0.038440) -1/26 EXTENDED HST (-0.039139,-0.034153) -4/109 HST (-0.036592,-0.036579) -3/82 EXTENDED HST (-0.036373,-0.036354) -2/55 EXTENDED HST (-0.035732,-0.035696) -1/28 EXTENDED HST (-0.036469,-0.031818) -7/205 HST (-0.034096,-0.034085) -3/88 EXTENDED HST (-0.033907,-0.033890) -2/59 EXTENDED HST (-0.033349,-0.033317) -1/30 EXTENDED HST (-0.035200,-0.028398) -9/283 HST (-0.031753,-0.031739) -2/63 EXTENDED HST (-0.031264,-0.031236) -1/32 EXTENDED HST (-0.030274,-0.026402) -4/141 HST (-0.028306,-0.028298) -3/106 EXTENDED HST (-0.028175,-0.028163) -2/71 EXTENDED HST (-0.027789,-0.027767) -1/36 EXTENDED HST (-0.029134,-0.023632) -9/341 HST (-0.026326,-0.026306) -1/38 EXTENDED HST (-0.023667,-0.023577) -3/127 HST (-0.023588,-0.023550) -7/297 HST (-0.025042,-0.022050) -15/637 HST (-0.023533,-0.023525) -2/85 EXTENDED HST (-0.022078,-0.022021) -37/1678 HST (-0.022050,-0.022003) -5/227 HST (-0.022808,-0.021185) -11/500 HST (-0.021981,-0.021975) -2/91 EXTENDED HST (-0.021746,-0.021732) -1/46 EXTENDED HST (-0.022597,-0.019697) -4/189 HST (-0.021129,-0.021125) -3/142 EXTENDED HST (-0.021056,-0.021049) -2/95 EXTENDED HST (-0.020840,-0.020827) -1/48 EXTENDED HST (-0.092511,0.113551 ) 0/1 EXTENDED HST The supplemental half-space computation shows that these NET maps are rational. SLOPE FUNCTION INFORMATION There are no slope function fixed points because every loop multiplier of the mod 2 slope correspondence graph is at least 1 and the map is rational. 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 |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,b,c^-1*b,c^-1*b,c^-1*b,1,1,1,1,1,1,1,1,c,b^-1*c,b^-1*c,b^-1*c>(2,17)(3,16)(4,15)(5,14)(6,13)(7,12)(8,11)(9,10)", "b=(1,17)(2,16)(3,15)(4,14)(5,13)(6,12)(7,11)(8,10)", "c=(1,17)(2,16)(3,15)(4,14)(5,13)(6,12)(7,11)(8,10)", "d=<1,c^-1,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,c,c,c,c*d>(2,17)(3,16)(4,15)(5,14)(6,13)(7,12)(8,11)(9,10)", "a*b*c*d"); When the translation term of the affine map is lambda1: NewSphereMachine( "a=(1,2)(3,17)(4,16)(5,15)(6,14)(7,13)(8,12)(9,11)", "b=<1,b,c^-1*b,c^-1*b,c^-1*b,1,1,1,1,1,1,1,1,c,b^-1*c,b^-1*c,b^-1*c>(2,17)(3,16)(4,15)(5,14)(6,13)(7,12)(8,11)(9,10)", "c=<1,c^-1,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,c,c,c,c*d>(2,17)(3,16)(4,15)(5,14)(6,13)(7,12)(8,11)(9,10)", "d=<1,1,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,1,c,c,c>(1,2)(3,17)(4,16)(5,15)(6,14)(7,13)(8,12)(9,11)", "a*b*c*d"); When the translation term of the affine map is lambda2: NewSphereMachine( "a=(1,16)(2,15)(3,14)(4,13)(5,12)(6,11)(7,10)(8,9)", "b=(1,17)(2,16)(3,15)(4,14)(5,13)(6,12)(7,11)(8,10)", "c=(1,17)(2,16)(3,15)(4,14)(5,13)(6,12)(7,11)(8,10)", "d=(1,16)(2,15)(3,14)(4,13)(5,12)(6,11)(7,10)(8,9)", "a*b*c*d"); When the translation term of the affine map is lambda1+lambda2: NewSphereMachine( "a=(1,17)(2,16)(3,15)(4,14)(5,13)(6,12)(7,11)(8,10)", "b=<1,c^-1,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,c,c,c,c*d>(2,17)(3,16)(4,15)(5,14)(6,13)(7,12)(8,11)(9,10)", "c=<1,b,c^-1*b,c^-1*b,c^-1*b,1,1,1,1,1,1,1,1,c,b^-1*c,b^-1*c,b^-1*c>(2,17)(3,16)(4,15)(5,14)(6,13)(7,12)(8,11)(9,10)", "d=(1,17)(2,16)(3,15)(4,14)(5,13)(6,12)(7,11)(8,10)", "a*b*c*d");