A space of cyclohedra
The Deligne-Knudsen-Mumford moduli space \(\overline{{\mathcal M}}^n_0\) of marked points on the sphere can be described as an iterated blow-up of the projective sphere \(\mathbb{P} V^{n-2}\) along certain cells \(m_k\), with a tiling by \({1\over 2}(n- 1)!\) associahedra \(K_{n-1}\). Guided by this result, the author defines \(\overline{{\mathcal Z}}^n\) as the iterated blow-up of the torus \(\mathbb{L} V^n\) along certain cells \(m_k\), and shows that it has a tiling by \((n-1)!\) cyclohedra \(W_n\). The paper contains a short exploration of the structure of this space and concludes with a discussion of its possible role in knot theory and mathematical physics.
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