The double-hendecagon trace-field direction conjecture

On the double-hendecagon translation surface, a direction is called hyperbolic or parabolic according to the corresponding type for the surface's Veech group, and the trace field is the trace field associated with that surface. Double-hendecagon direction conjecture. There are no hyperbolic directions in the trace field, and there are directions in the trace field that are not parabolic or hyperbolic. This conjecture proposes a contrast with the double-heptagon case; the supplied text gives no evidence of a resolution and says only that the conjectures were suggested by tests and that the same ideas appeared in earlier work.