Cyclohedron

In geometry, the cyclohedron is a d-dimensional polytope where d can be any non-negative integer.

It was first introduced as a combinatorial object by Raoul Bott and Clifford Taubes[1] and, for this reason, it is also sometimes called the Bott–Taubes polytope.

It was later constructed as a polytope by Martin Markl[2] and by Rodica Simion.

[3] Rodica Simion describes this polytope as an associahedron of type B.

The cyclohedron appears in the study of knot invariants.

[4] Cyclohedra belong to several larger families of polytopes, each providing a general construction.

For instance, the cyclohedron belongs to the generalized associahedra[5] that arise from cluster algebra, and to the graph-associahedra,[6] a family of polytopes each corresponding to a graph.

Just as the associahedron, the cyclohedron can be recovered by removing some of the facets of the permutohedron.

-dimensional cyclohedron is the flip graph of the centrally symmetric partial triangulations of a convex polygon with

goes to infinity, the asymptotic behavior of the diameter