2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/60980The real points of the Deligne-Knudsen-Mumford moduli space of marked points on the sphere has a natural tiling by associahedra. We extend this idea to create a moduli space tiled by cyclohedra. We explore the structure of this space, coming from blow-ups of hyperplane arrangements, as well as discuss possibilities of its role in knot theory and mathematical physics.18 pages, 18 figures, LaTex2eQuantum AlgebraAlgebraic GeometryGeometric TopologyPrimary 14P25, Secondary 05B45, 52B11text