Caoduro–Khodamoradi–Paat–Shepherd simplex exchange conjecture

Let $S$ and $T$ be $d$-dimensional simplices whose interiors contain the origin. A vertex exchange replaces one vertex while producing another $d$-dimensional simplex whose interior contains the origin. Caoduro–Khodamoradi–Paat–Shepherd's simplex exchange conjecture. Any two such simplices can be transformed into each other via at most $d+1$ vertex exchanges, while always maintaining the origin in the interior. The paper's abstract states that this conjecture is disproved.