3 problems

Cone-type minimality conjecture. If $\tau$ has no bad cycle, then the cone-type triangulation at a degree-$6$ vertex is minimal, and

Flip–tetrahedral ratio conjecture. This ratio cannot exceed, or attain, $\frac{3}{2}$.

Dehnhardt's conjecture. The pair $D_n$ has flip distance $2n-10$ when $n$ is greater than $9$.