These Thurston maps are NET maps for every choice of translation term. They have degree 27. They are imprimitive, each factoring as a NET map with degree 9 followed by a Euclidean NET map with degree 3. 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 0/3, 0/9, 0/27, 1/27, 3/9, 3/3, 3/1, 6/1, 12/1, 15/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-infinity,-1.322105) (-1.320864,-1.319007) (-1.316307,-1.315240) (-1.308783,-1.250000) (-1.244359,-1.214286) (-1.211088,-1.210019) (-1.207133,-1.206675) (-1.205258,-1.205005) (-1.195234,-1.195005) (-1.193743,-1.193342) (-1.190893,-1.190019) (-1.188076,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 (-1.322894,-1.318960) -37/28 EXTENDED HST -> HST (-1.319545,-1.313522) -29/22 EXTENDED HST -> HST (-1.313758,-1.313286) -2409/1834 HST (-1.313522,-1.313203) -88/67 HST (-1.313392,-1.313112) -239/182 HST (-1.313145,-1.312941) -130/99 HST (-1.313005,-1.312845) -193/147 HST (-1.312852,-1.312740) -256/195 HST (-1.312770,-1.312684) -361/275 HST (-1.312701,-1.312636) -466/355 HST (-1.312659,-1.312608) -613/467 HST (-1.312625,-1.312585) -760/579 HST (-1.312599,-1.312567) -970/739 HST (-1.312583,-1.312416) -21/16 EXTENDED HST (-1.312423,-1.312386) -857/653 HST (-1.312404,-1.312358) -710/541 HST (-1.312383,-1.312326) -563/429 HST (-1.312349,-1.312276) -458/349 HST (-1.312313,-1.312222) -353/269 HST (-1.312254,-1.312135) -290/221 HST (-1.312209,-1.312068) -248/189 HST (-1.312144,-1.311969) -185/141 HST (-1.312039,-1.311813) -143/109 HST (-1.311849,-1.311525) -101/77 HST (-1.311603,-1.311147) -80/61 HST (-1.311393,-1.310822) -59/45 HST (-1.315993,-1.305542) -97/74 HST (-1.310418,-1.309272) -38/29 EXTENDED HST -> HST (-1.250449,-1.249558) -5/4 EXTENDED HST (-1.249641,-1.249467) -706/565 HST (-1.249557,-1.249349) -571/457 HST (-1.249451,-1.249194) -466/373 HST (-1.249329,-1.248984) -371/297 HST (-1.249157,-1.249058) -351/281 HST (-1.249099,-1.248681) -286/229 HST (-1.248892,-1.245229) -116/93 HST (-1.247228,-1.241015) -56/45 HST (-1.217051,-1.208153) -17/14 EXTENDED HST -> HST (-1.210554,-1.204903) -64/53 HST (-1.205990,-1.202728) -53/44 HST (-1.202898,-1.196969) -6/5 EXTENDED HST (-1.197261,-1.193670) -55/46 HST (-1.195062,-1.188341) -31/26 EXTENDED HST -> HST (-1.188367,-1.188101) -101/85 HST (-1.188438,-1.187746) -379/319 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. FUNDAMENTAL GROUP WREATH RECURSIONS When the translation term of the affine map is 0: NewSphereMachine( "a=(2,27)(3,26)(4,25)(5,24)(6,23)(7,22)(8,21)(9,20)(10,19)(11,18)(12,17)(13,16)(14,15)", "b=(1,27)(2,26)(3,25)(4,24)(5,23)(6,22)(7,21)(8,20)(9,19)(10,18)(11,17)(12,16)(13,15)", "c=(1,27)(2,26)(3,25)(4,24)(5,23)(6,22)(7,21)(8,20)(9,19)(10,18)(11,17)(12,16)(13,15)", "d=<1,a*b,a*b,a*b,a*b,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c,c,c*d,c*d,c*d,c*d>(2,27)(3,26)(4,25)(5,24)(6,23)(7,22)(8,21)(9,20)(10,19)(11,18)(12,17)(13,16)(14,15)", "a*b*c*d"); When the translation term of the affine map is lambda1: NewSphereMachine( "a=(1,2)(3,27)(4,26)(5,25)(6,24)(7,23)(8,22)(9,21)(10,20)(11,19)(12,18)(13,17)(14,16)", "b=(2,27)(3,26)(4,25)(5,24)(6,23)(7,22)(8,21)(9,20)(10,19)(11,18)(12,17)(13,16)(14,15)", "c=<1,a*b,a*b,a*b,a*b,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,c,c,c,c*d,c*d,c*d,c*d>(2,27)(3,26)(4,25)(5,24)(6,23)(7,22)(8,21)(9,20)(10,19)(11,18)(12,17)(13,16)(14,15)", "d=<1,1,a*b,a*b,a*b,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,c,c,c*d,c*d,c*d,c*d>(1,2)(3,27)(4,26)(5,25)(6,24)(7,23)(8,22)(9,21)(10,20)(11,19)(12,18)(13,17)(14,16)", "a*b*c*d"); When the translation term of the affine map is lambda2: NewSphereMachine( "a=(1,26)(2,25)(3,24)(4,23)(5,22)(6,21)(7,20)(8,19)(9,18)(10,17)(11,16)(12,15)(13,14)", "b=(1,27)(2,26)(3,25)(4,24)(5,23)(6,22)(7,21)(8,20)(9,19)(10,18)(11,17)(12,16)(13,15)", "c=(1,27)(2,26)(3,25)(4,24)(5,23)(6,22)(7,21)(8,20)(9,19)(10,18)(11,17)(12,16)(13,15)", "d=(1,26)(2,25)(3,24)(4,23)(5,22)(6,21)(7,20)(8,19)(9,18)(10,17)(11,16)(12,15)(13,14)", "a*b*c*d"); When the translation term of the affine map is lambda1+lambda2: NewSphereMachine( "a=(1,27)(2,26)(3,25)(4,24)(5,23)(6,22)(7,21)(8,20)(9,19)(10,18)(11,17)(12,16)(13,15)", "b=<1,a*b,a*b,a*b,a*b,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,c,c,c,c*d,c*d,c*d,c*d>(2,27)(3,26)(4,25)(5,24)(6,23)(7,22)(8,21)(9,20)(10,19)(11,18)(12,17)(13,16)(14,15)", "c=(2,27)(3,26)(4,25)(5,24)(6,23)(7,22)(8,21)(9,20)(10,19)(11,18)(12,17)(13,16)(14,15)", "d=(1,27)(2,26)(3,25)(4,24)(5,23)(6,22)(7,21)(8,20)(9,19)(10,18)(11,17)(12,16)(13,15)", "a*b*c*d");