The asymptotic diameter of cyclohedra

AbstractIt is shown here that the diameter of the d-dimensional cyclohedron is not greater than ⌈5d/2⌉ − 2. It is also shown that the 5/2 coefficient in this upper bound is asymptotically sharp. More precisely, the d-dimensional cyclohedron has diameter at least 5d/24d45d/2−4d−4 .