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}
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 12.
ALL THURSTON MULTIPLIERS c/d IN UNREDUCED FORM
0/1, 0/5, 1/5, 1/1
EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION
(-88.641833,0.000000 )
( 0.000000,0.400000 )
( 0.400000,0.500000 )
( 0.500000,2.000000 )
( 2.000000,88.641833)
The half-space computation does not determine rationality.
EXCLUDED INTERVALS FOR JUST THE SUPPLEMENTAL HALF-SPACE COMPUTATION
INTERVAL COMPUTED FOR HST OR EXTENDED HST
(-0.071429,0.062504) 0/1 EXTENDED HST
( 0.367190,0.439362) 2/5 EXTENDED HST
( 0.478599,0.523411) 1/2 EXTENDED HST
( 1.835845,2.196507) 2/1 EXTENDED HST
-2.235352)(2.236328 infinity EXTENDED 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 |p'| <= |p|
for every slope p/q with |p| <= 50 and |q| <= 50.
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=<1,d^-1,d*a,1,1>(2,3)(4,5)",
"b=<1,b,1,1,c>(2,3)(4,5)",
"c=<1,d,1,1,1>(1,2)(3,4)",
"d=<1,1,c^-1,c,1>(1,2)(3,4)",
"a*b*c*d");
When the translation term of the affine map is lambda1:
NewSphereMachine(
"a=<1,d^-1,b*d,b*c*b^-1,1>(2,3)(4,5)",
"b=<1,a,1,1,1>(2,3)(4,5)",
"c=<1,1,1,1,1>(1,2)(3,4)",
"d=(1,2)(3,4)",
"a*b*c*d");
When the translation term of the affine map is lambda2:
NewSphereMachine(
"a=(1,2)(3,4)",
"b=<1,d,1,1,1>(1,2)(3,4)",
"c=<1,b,1,1,c>(2,3)(4,5)",
"d=<1,c^-1,b^-1*d^-1,c^-1,c>(2,3)(4,5)",
"a*b*c*d");
When the translation term of the affine map is lambda1+lambda2:
NewSphereMachine(
"a=<1,d,b*c*b^-1,b*d*a,1>(1,2)(3,4)",
"b=<1,1,1,1,1>(1,2)(3,4)",
"c=<1,a,1,1,1>(2,3)(4,5)",
"d=<1,b*d*a,b*c,1,b*c*b^-1>(2,3)(4,5)",
"a*b*c*d");