The -dimensional cyclohedron and the correspondence between its vertices and edges with a cycle on three vertices
In geometry, the cyclohedron is a -dimensional polytope where 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]
^Bott, Raoul; Taubes, Clifford (1994). "On the self‐linking of knots". Journal of Mathematical Physics. 35 (10): 5247–5287. doi:10.1063/1.530750. MR 1295465.
^Markl, Martin (1999). "Simplex, associahedron, and cyclohedron". Contemporary Mathematics. 227: 235–265. doi:10.1090/conm/227. ISBN 9780821809136. MR 1665469.
^Simion, Rodica (2003). "A type-B associahedron". Advances in Applied Mathematics. 30 (1–2): 2–25. doi:10.1016/S0196-8858(02)00522-5.
^Stasheff, Jim (1997), "From operads to 'physically' inspired theories", in Loday, Jean-Louis; Stasheff, James D.; Voronov, Alexander A. (eds.), Operads: Proceedings of Renaissance Conferences, Contemporary Mathematics, vol. 202, AMS Bookstore, pp. 53–82, ISBN 978-0-8218-0513-8, archived from the original on 23 May 1997, retrieved 1 May 2011
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