These Thurston maps are NET maps for every choice of translation term.
They have degree 9. They are imprimitive, each factoring as a NET map
with degree 3 followed by a Euclidean NET map with degree 3.
PURE MODULAR GROUP HURWITZ EQUIVALENCE CLASSES FOR TRANSLATIONS
{0} {lambda1,lambda1+lambda2} {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 10.
ALL THURSTON MULTIPLIERS c/d IN UNREDUCED FORM
1/3, 3/3
EXCLUDED INTERVALS FOR THE HALF-SPACE COMPUTATION
(-49.577350,-48.422650)
(-47.577350,-46.422650)
(-45.577350,-44.422650)
(-43.577350,-42.422650)
(-41.577350,-40.422650)
(-39.577350,-38.422650)
(-37.577350,-36.422650)
(-35.577350,-34.422650)
(-33.577350,-32.422650)
(-31.577350,-30.422650)
(-29.577350,-28.422650)
(-27.577350,-26.422650)
(-25.577350,-24.297086)
(-23.702914,-22.297086)
(-21.702914,-20.297086)
(-19.702914,-18.297086)
(-17.702914,-16.000000)
(-16.000000,-14.000000)
(-14.000000,-12.000000)
(-12.000000,-10.000000)
(-10.000000,-8.000000 )
( -8.000000,-6.000000 )
( -6.000000,-4.000000 )
( -4.000000,-2.000000 )
( -2.000000,0.000000 )
( 0.000000,2.000000 )
( 2.000000,4.000000 )
( 4.000000,6.000000 )
( 6.000000,8.000000 )
( 8.000000,10.000000 )
( 10.000000,12.000000 )
( 12.000000,14.000000 )
( 14.000000,16.000000 )
( 16.000000,17.702914 )
( 18.297086,19.702914 )
( 20.297086,21.702914 )
( 22.297086,23.702914 )
( 24.297086,25.577350 )
( 26.422650,27.577350 )
( 28.422650,29.577350 )
( 30.422650,31.577350 )
( 32.422650,33.577350 )
( 34.422650,35.577350 )
( 36.422650,37.577350 )
( 38.422650,39.577350 )
( 40.422650,41.577350 )
( 42.422650,43.577350 )
( 44.422650,45.577350 )
( 46.422650,47.577350 )
( 48.422650,49.577350 )
0/1 is the slope of a Thurston obstruction with c = 3 and d = 3.
These NET maps are not rational.
SLOPE FUNCTION INFORMATION
EQUATOR?
FIXED POINT c d 0 lambda1 lambda2 lambda1+lambda2
0/1 3 3 No No No No
1/2N 1 3 No No No No
There are no more slope function fixed points.
Number of excluded intervals computed by the fixed point finder: 298
There are no equators because both elementary divisors are greater than 1.
No nontrivial cycles were found.
The slope function maps every slope to a slope:
no slope maps to the nonslope.
If the slope function maps slope s to a slope s' and
if the intersection pairing of s with 0/1 is n, then
the intersection pairing of s' with 0/1 is at most n.
The slope function orbit of every slope whose intersection
pairing with 0/1 is at most 50 ends in one of the
slopes described above.
FUNDAMENTAL GROUP WREATH RECURSIONS
When the translation term of the affine map is 0:
NewSphereMachine(
"a=(2,6)(3,8)(4,7)(5,9)",
"b=**(1,7)(2,3)(5,6)(8,9)",
"c=<1,1,1,1,1,1,1,1,c>(1,2)(3,9)(4,5)(7,8)",
"d=(1,8)(2,4)(5,7)(6,9)",
"a*b*c*d");
When the translation term of the affine map is lambda1:
NewSphereMachine(
"a=(1,4)(2,6)(3,8)(5,9)",
"b=(2,3)(4,7)(5,6)(8,9)",
"c=<1,1,d,1,1,1,1,1,1>(1,2)(4,5)(6,9)(7,8)",
"d=(1,8)(2,4)(3,6)(5,7)",
"a*b*c*d");
When the translation term of the affine map is lambda2:
NewSphereMachine(
"a=<1,a*b,1,1,1,1,c*d,1,c*d*c^-1>(1,5)(2,7)(3,6)(4,8)",
"b=<1,1,1,1,1,1,1,1,c>(1,2)(3,9)(4,5)(7,8)",
"c=****(1,7)(2,3)(5,6)(8,9)",
"d=<1,a*b,1,1,1,1,b^-1*a*b,1,c*d>(1,4)(2,9)(3,5)(6,8)",
"a*b*c*d");
When the translation term of the affine map is lambda1+lambda2:
NewSphereMachine(
"a=<1,a*b,1,1,1,1,c*d,1,c>(1,5)(2,7)(3,9)(4,8)",
"b=<1,1,d,1,1,1,1,1,1>(1,2)(4,5)(6,9)(7,8)",
"c=(2,3)(4,7)(5,6)(8,9)",
"d=****(1,7)(2,9)(3,5)(6,8)",
"a*b*c*d");
**