These Thurston maps are NET maps for every choice of translation term. They have degree 25. They are imprimitive, each factoring as a NET map with degree 5 followed by a Euclidean NET map with degree 5. 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, 0/5, 0/25, 1/25, 5/5, 5/1, 10/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-infinity,-0.833333) (-0.833333,-0.416667) (-0.416667,-0.138889) (-0.138889,-0.131579) (-0.131579,-0.125000) (-0.125000,-0.119048) (-0.119048,-0.113636) (-0.113636,-0.108696) (-0.108696,-0.104167) (-0.104167,-0.100000) (-0.097403,-0.096154) (-0.092593,-0.089286) (-0.086207,-0.085227) (-0.081522,-0.080645) (-0.078125,-0.075758) (-0.073529,-0.072816) (-0.070093,-0.069444) (-0.067568,-0.065789) (-0.064103,-0.063559) (-0.061475,-0.060976) (-0.059524,-0.058140) (-0.053191,-0.052083) (-0.048077,-0.047170) (-0.043860,-0.043103) (-0.040323,-0.039683) (-0.037313,-0.036765) (-0.034722,-0.034247) (-0.032468,-0.032051) (-0.030488,-0.030120) (-0.028736,-0.028409) (-0.027174,-0.026882) (-0.025773,-0.025510) (-0.024510,-0.024272) (-0.023364,-0.023148) (-0.022321,-0.022124) (-0.021368,-0.021186) (-0.020492,-0.020325) ( 0.020325,0.020492 ) ( 0.021186,0.021368 ) ( 0.022124,0.022321 ) ( 0.023148,0.023364 ) ( 0.024272,0.024510 ) ( 0.025510,0.025773 ) ( 0.026882,0.027174 ) ( 0.028409,0.028736 ) ( 0.030120,0.030488 ) ( 0.032051,0.032468 ) ( 0.034247,0.034722 ) ( 0.036765,0.037313 ) ( 0.039683,0.040323 ) ( 0.043103,0.043860 ) ( 0.047170,0.048077 ) ( 0.052083,0.053191 ) ( 0.058140,0.059524 ) ( 0.060976,0.061475 ) ( 0.063559,0.064103 ) ( 0.065789,0.067568 ) ( 0.069444,0.070093 ) ( 0.072816,0.073529 ) ( 0.075758,0.078125 ) ( 0.080645,0.081522 ) ( 0.085227,0.086207 ) ( 0.089286,0.092593 ) ( 0.096154,0.097403 ) ( 0.100000,0.104167 ) ( 0.104167,0.108696 ) ( 0.108696,0.113636 ) ( 0.113636,0.119048 ) ( 0.119048,0.125000 ) ( 0.125000,0.131579 ) ( 0.131579,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 (-0.836644,-0.829977) -5/6 EXTENDED HST (-0.417497,-0.415830) -5/12 EXTENDED HST (-0.143411,-0.130952) -5/36 EXTENDED HST -> HST (-0.125125,-0.124875) -1/8 EXTENDED HST (-0.121795,-0.114719) -5/42 EXTENDED HST -> HST (-0.118966,-0.107018) -5/44 EXTENDED HST -> HST (-0.108365,-0.101145) -5/48 EXTENDED HST -> HST (-0.100080,-0.099920) -1/10 EXTENDED HST (-0.100000,-0.096154) -4/41 EXTENDED HST -> HST (-0.098616,-0.092657) -5/52 HST (-0.096154,-0.092593) -2/21 EXTENDED HST -> HST (-0.097183,-0.087143) -5/54 HST (-0.088543,-0.085431) -125/1437 HST (-0.086987,-0.086926) -2/23 EXTENDED HST (-0.086207,-0.083333) -4/47 EXTENDED HST -> HST (-0.083389,-0.083278) -1/12 EXTENDED HST (-0.083333,-0.080645) -4/49 EXTENDED HST -> HST (-0.082849,-0.077713) -5/62 HST (-0.080645,-0.078125) -2/25 EXTENDED HST -> HST (-0.079060,-0.071429) -5/66 HST (-0.071469,-0.071388) -1/14 EXTENDED HST (-0.071429,-0.069444) -4/57 HST (-0.071429,-0.066919) -5/72 HST (-0.069444,-0.067568) -2/29 EXTENDED HST -> HST (-0.068773,-0.062030) -5/76 HST (-0.062500,-0.060976) -4/65 HST (-0.062775,-0.058758) -5/82 HST (-0.060976,-0.059524) -2/33 EXTENDED HST -> HST (-0.060855,-0.054817) -5/86 HST (-0.055580,-0.055531) -1/18 EXTENDED HST (-0.055556,-0.054348) -4/73 HST (-0.054745,-0.054348) -3/55 HST (-0.055992,-0.052372) -5/92 HST (-0.054348,-0.053191) -2/37 EXTENDED HST -> HST (-0.054572,-0.049107) -5/96 HST (-0.050020,-0.049980) -1/20 EXTENDED HST (-0.050532,-0.047237) -5/102 HST (-0.049020,-0.048077) -2/41 EXTENDED HST -> HST (-0.049465,-0.044474) -5/106 HST (-0.045471,-0.045438) -1/22 EXTENDED HST (-0.044643,-0.043860) -2/45 EXTENDED HST -> HST (-0.046309,-0.041216) -5/114 HST (-0.041229,-0.041168) -15/364 HST (-0.041209,-0.040984) -3/73 HST (-0.042285,-0.039493) -5/122 HST (-0.040984,-0.040323) -2/49 EXTENDED HST -> HST (-0.039683,-0.039062) -3/76 HST (-0.039222,-0.039210) -2/51 EXTENDED HST (-0.040541,-0.037749) -5/128 HST (-0.039062,-0.038860) -3/77 HST (-0.038473,-0.038450) -1/26 EXTENDED HST (-0.037879,-0.037313) -2/53 HST (-0.039429,-0.035057) -5/134 HST (-0.036702,-0.032620) -5/144 HST (-0.034328,-0.030500) -5/154 HST (-0.032243,-0.028638) -5/164 HST (-0.029887,-0.026786) -5/176 HST (-0.027784,-0.027772) -1/36 EXTENDED HST (-0.026882,-0.026596) -3/112 HST (-0.027590,-0.025678) -5/188 HST (-0.026596,-0.026502) -3/113 HST (-0.026321,-0.026310) -1/38 EXTENDED HST (-0.026851,-0.024052) -5/196 HST (-0.025005,-0.024995) -1/40 EXTENDED HST (-0.024934,-0.023205) -5/208 HST (-0.024038,-0.023962) -3/125 HST (-0.023814,-0.023805) -1/42 EXTENDED HST (-0.024374,-0.021825) -5/216 HST (-0.022731,-0.022723) -1/44 EXTENDED HST (-0.023067,-0.020548) -6/275 HST (-0.021743,-0.021735) -1/46 EXTENDED HST (-0.021688,-0.019366) -3/146 HST (-0.058824,0.066675 ) 0/1 EXTENDED HST ( 0.063707,0.072266 ) 5/74 HST ( 0.068946,0.068985 ) 2/29 EXTENDED HST ( 0.071429,0.073529 ) 4/55 HST ( 0.070930,0.081176 ) 5/66 HST ( 0.080645,0.083333 ) 4/49 EXTENDED HST -> HST ( 0.083278,0.083389 ) 1/12 EXTENDED HST ( 0.083333,0.086207 ) 4/47 EXTENDED HST -> HST ( 0.083562,0.095833 ) 5/56 HST ( 0.092014,0.099303 ) 5/52 HST ( 0.098684,0.100000 ) 15/151 HST ( 0.099920,0.100080 ) 1/10 EXTENDED HST ( 0.100379,0.109195 ) 5/48 EXTENDED HST -> HST ( 0.107143,0.122517 ) 5/44 EXTENDED HST -> HST ( 0.124875,0.125125 ) 1/8 EXTENDED HST ( 0.126794,0.138350 ) 5/38 EXTENDED HST -> 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=(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=(1,25)(2,24)(3,23)(4,22)(5,21)(6,20)(7,19)(8,18)(9,17)(10,16)(11,15)(12,14)", "c=(1,25)(2,24)(3,23)(4,22)(5,21)(6,20)(7,19)(8,18)(9,17)(10,16)(11,15)(12,14)", "d=<1,a*b,a*b,c^-1,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,c,c,c,c,c*d,c*d>(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: NewSphereMachine( "a=(1,2)(3,25)(4,24)(5,23)(6,22)(7,21)(8,20)(9,19)(10,18)(11,17)(12,16)(13,15)", "b=(2,25)(3,24)(4,23)(5,22)(6,21)(7,20)(8,19)(9,18)(10,17)(11,16)(12,15)(13,14)", "c=<1,a*b,a*b,c^-1,c^-1,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,c,c,c,c,c,c*d,c*d>(2,25)(3,24)(4,23)(5,22)(6,21)(7,20)(8,19)(9,18)(10,17)(11,16)(12,15)(13,14)", "d=<1,1,a*b,c^-1,c^-1,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,1,c,c,c,c,c*d,c*d>(1,2)(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"); When the translation term of the affine map is lambda2: NewSphereMachine( "a=(1,24)(2,23)(3,22)(4,21)(5,20)(6,19)(7,18)(8,17)(9,16)(10,15)(11,14)(12,13)", "b=(1,25)(2,24)(3,23)(4,22)(5,21)(6,20)(7,19)(8,18)(9,17)(10,16)(11,15)(12,14)", "c=(1,25)(2,24)(3,23)(4,22)(5,21)(6,20)(7,19)(8,18)(9,17)(10,16)(11,15)(12,14)", "d=(1,24)(2,23)(3,22)(4,21)(5,20)(6,19)(7,18)(8,17)(9,16)(10,15)(11,14)(12,13)", "a*b*c*d"); When the translation term of the affine map is lambda1+lambda2: NewSphereMachine( "a=(1,25)(2,24)(3,23)(4,22)(5,21)(6,20)(7,19)(8,18)(9,17)(10,16)(11,15)(12,14)", "b=<1,a*b,a*b,c^-1,c^-1,c^-1,c^-1,c^-1,1,1,1,1,1,1,1,1,1,1,c,c,c,c,c,c*d,c*d>(2,25)(3,24)(4,23)(5,22)(6,21)(7,20)(8,19)(9,18)(10,17)(11,16)(12,15)(13,14)", "c=(2,25)(3,24)(4,23)(5,22)(6,21)(7,20)(8,19)(9,18)(10,17)(11,16)(12,15)(13,14)", "d=(1,25)(2,24)(3,23)(4,22)(5,21)(6,20)(7,19)(8,18)(9,17)(10,16)(11,15)(12,14)", "a*b*c*d");