These Thurston maps are NET maps for every choice of translation term. They are primitive and have degree 26. PURE MODULAR GROUP HURWITZ EQUIVALENCE CLASSES FOR TRANSLATIONS {0} {lambda1} {lambda2} {lambda1+lambda2} These pure modular group Hurwitz classes each contain 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 0/2, 0/26, 1/26, 1/13, 1/2, 1/1, 2/2, 3/2, 2/1, 5/2, 3/1, 6/2, 4/1, 9/2 5/1, 6/1, 7/1, 9/1, 12/1, 13/1, 16/1 EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION (-infinity,-1.169367) (-1.163474,-1.162014) (-1.161662,-1.156501) (-1.154910,-1.152570) (-1.152056,-1.151034) (-1.148922,-1.147304) (-1.146661,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 (-1.169956,-1.168512) -76/65 HST (-1.168831,-1.168317) -215/184 HST (-1.168443,-1.168400) -111/95 HST (-1.168891,-1.167800) -118/101 HST (-1.168082,-1.167483) -174/149 HST (-1.167671,-1.167251) -244/209 HST (-1.167493,-1.167012) -335/287 HST (-1.167090,-1.166252) -7/6 EXTENDED HST (-1.166301,-1.166027) -386/331 HST (-1.166157,-1.165755) -274/235 HST (-1.165957,-1.165877) -260/223 HST (-1.165903,-1.165894) -253/217 HST (-1.165882,-1.164972) -155/133 HST (-1.165363,-1.164291) -106/91 HST (-1.164786,-1.162993) -78/67 HST (-1.163986,-1.163881) -71/61 HST (-1.163758,-1.163563) -64/55 HST (-1.162496,-1.161400) -208/179 HST (-1.161995,-1.161791) -122/105 HST (-1.161772,-1.161758) -79/68 EXTENDED HST (-1.156863,-1.153846) -37/32 EXTENDED HST -> HST (-1.152617,-1.152458) -68/59 HST (-1.152599,-1.152135) -121/105 HST (-1.152189,-1.152159) -53/46 EXTENDED HST (-1.152157,-1.151992) -250/217 HST (-1.151285,-1.150586) -61/53 HST (-1.150899,-1.150124) -107/93 HST (-1.150168,-1.150074) -475/413 HST (-1.150094,-1.150054) -1571/1366 HST (-1.150073,-1.150072) -797/693 HST (-1.150075,-1.150033) -1073/933 HST (-1.150038,-1.149962) -23/20 EXTENDED HST (-1.150142,-1.149572) -468/407 HST (-1.149873,-1.149779) -330/287 HST (-1.149824,-1.149694) -238/207 HST (-1.149738,-1.149727) -215/187 HST (-1.149711,-1.149505) -146/127 HST (-1.149601,-1.149234) -100/87 HST (-1.149295,-1.149207) -77/67 HST (-1.149246,-1.149167) -362/315 HST (-1.149198,-1.148695) -54/47 HST (-1.147400,-1.146679) -39/34 EXTENDED HST (-1.146768,-1.146571) -86/75 HST The supplemental half-space computation shows that these NET maps are rational. SLOPE FUNCTION INFORMATION NUMBER OF FIXED POINTS: 1 EQUATOR? FIXED POINT c d 0 lambda1 lambda2 lambda1+lambda2 5/6 1 13 No No No No NUMBER OF EQUATORS: 0 0 0 0 There are no more slope function fixed points. Number of excluded intervals computed by the fixed point finder: 5112 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 either one of the above cycles or the nonslope. FUNDAMENTAL GROUP WREATH RECURSIONS When the translation term of the affine map is 0: NewSphereMachine( "a=(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=(1,26)(2,25)(3,24)(4,23)(5,22)(6,21)(7,20)(8,19)(9,18)(10,17)(11,16)(12,15)(13,14)", "c=(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)", "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,c,c*d,c*d,c*d,c*d,c*d>(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"); When the translation term of the affine map is lambda1: NewSphereMachine( "a=(1,2)(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=(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,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,c,c*d,c*d,c*d,c*d,c*d>(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=<1,1,a*b,a*b,a*b,a*b,c^-1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,c,c*d,c*d,c*d,c*d>(1,2)(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 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=(1,26)(2,25)(3,24)(4,23)(5,22)(6,21)(7,20)(8,19)(9,18)(10,17)(11,16)(12,15)(13,14)", "c=(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)", "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"); When the translation term of the affine map is lambda1+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,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,c,c*d,c*d,c*d,c*d,c*d>(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=(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");