These Thurston maps are NET maps for every choice of translation term.
They are primitive and have degree 5.
PURE MODULAR GROUP HURWITZ EQUIVALENCE CLASSES FOR TRANSLATIONS
{0} {lambda1} {lambda2} {lambda1+lambda2}
Since no Thurston multiplier is 1, this modular group Hurwitz class
contains only finitely 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
0/5, 2/1
EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION
(-infinity,-0.086148)
( 0.080065, infinity)
1/0 is the slope of a Thurston obstruction with c = 2 and d = 1.
These NET maps are not rational.
SLOPE FUNCTION CYCLES FOUND
NUMBER OF FIXED POINTS FOUND: 1 EQUATOR?
FIXED POINTS c d 0 lambda1 lambda2 lambda1+lambda2
1/0 2 1 No No No No
NUMBER OF EQUATORS FOUND: 0 0 0 0
No nontrivial cycles were found.
The slope function maps some slope to the nonslope.
If the slope function maps slope s to a slope s' and
if the intersection pairing of s with 1/0 is n, then
the intersection pairing of s' with 1/0 is at most n.
The slope function orbit of every slope whose intersection
pairing with 1/0 is at most 50 ends in either the
nonslope or one of the slopes described above.
FUNDAMENTAL GROUP WREATH RECURSIONS
When the translation term of the affine map is 0:
NewSphereMachine(
"a=(1,4)(2,3)",
"b=(1,5)(2,4)",
"c=(1,5)(2,4)",
"d=(1,4)(2,3)",
"a*b*c*d");
When the translation term of the affine map is lambda1:
NewSphereMachine(
"a=(1,2)(3,5)",
"b=<1,b,b,b^-1,b^-1>(2,5)(3,4)",
"c=(2,5)(3,4)",
"d=(1,2)(3,5)",
"a*b*c*d");
When the translation term of the affine map is lambda2:
NewSphereMachine(
"a=(2,5)(3,4)",
"b=(1,5)(2,4)",
"c=(1,5)(2,4)",
"d=<1,d*c^-1,d*a*c^-1,c*b*c,c*d^-1>(2,5)(3,4)",
"a*b*c*d");
When the translation term of the affine map is lambda1+lambda2:
NewSphereMachine(
"a=(1,5)(2,4)",
"b=(2,5)(3,4)",
"c=<1,b,b,b^-1,b^-1>(2,5)(3,4)",
"d=(1,5)(2,4)",
"a*b*c*d");