These Thurston maps are NET maps for every choice of translation term.
They are primitive and have degree 25.
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 7.
ALL THURSTON MULTIPLIERS c/d IN UNREDUCED FORM
1/25, 1/5, 3/5, 1/1, 3/1, 7/1, 9/1, 11/1, 13/1, 17/1, 19/1, 21/1, 23/1
Every NET map in these pure modular group Hurwitz classes is
rational because the modulo 2 correspondence graph has no loops.
EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION
(-infinity,-0.046032)
(-0.045614,infinity )
SLOPE FUNCTION INFORMATION
There are no slope function fixed points because
the mod 2 slope correspondence graph has no loops.
NONTRIVIAL CYCLES
5092/233 -> 29503/1350 -> 14227/651 -> 5092/233
19319/884 -> 24411/1117 -> 23362/1069 -> 39687/1816 ->
81319/3721 -> 33546/1535 -> 19319/884
The slope function maps every slope to a slope:
no slope maps to the nonslope.
There are 3096 slopes s = p/q with |p| <= 50 and |q| <= 50.
The 14 slopes s in the following list have the property that the
slope function orbit of s contains a slope t whose numerator or
denominator exceeds 1,000,000 in absolute value, and the slopes between
s and t are not among the slopes p/q with |p| <= 50 and |q| <= 50.
49/2, -20/7, 1/11, -44/13, -40/13, -36/13, -48/17, -44/17, -8/21, -12/29,
-36/37, -11/37, -16/41, -48/49
The slope function orbit of every slope p/q with |p| <= 50 and |q| <= 50
either contains an extended rational number whose numerator or
denominator exceeds 1,000,000 in absolute value or ends in one of the above cycles.
FUNDAMENTAL GROUP WREATH RECURSIONS
When the translation term of the affine map is 0:
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=(1,24)(2,23)(3,22)(4,21)(5,20)(6,19)(7,18)(8,17)(9,16)(10,15)(11,14)(12,13)",
"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=(1,25)(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:
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,a*b,b,b,b,b,b,b,b,b,b,b,b,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1>(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=(1,25)(2,24)(3,23)(4,22)(5,21)(6,20)(7,19)(8,18)(9,17)(10,16)(11,15)(12,14)",
"d=(1,25)(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 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=(1,25)(2,24)(3,23)(4,22)(5,21)(6,20)(7,19)(8,18)(9,17)(10,16)(11,15)(12,14)",
"c=(1,24)(2,23)(3,22)(4,21)(5,20)(6,19)(7,18)(8,17)(9,16)(10,15)(11,14)(12,13)",
"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=(1,25)(2,24)(3,23)(4,22)(5,21)(6,20)(7,19)(8,18)(9,17)(10,16)(11,15)(12,14)",
"c=<1,a*b,b,b,b,b,b,b,b,b,b,b,b,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1,b^-1>(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=(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");