We describe a new sequence of polytopes which characterize $A_{infty}$-maps from a topological monoid to an $A_{infty}$-space. Therefore each of these polytopes is a quotient of the corresponding multiplihedron. Our sequence of polytopes is demonstrated not to be combinatorially equivalent to the associahedra, as was previously assumed in both topological and categorical literature. They are given the new collective name composihedra. We point out how these polytopes are used to parametrize compositions in the formulation of the theories of enriched bicategories and pseudomonoids in a monoidal bicategory. We also present a simple algorithm for determining the extremal points in Euclidean space whose convex hull is the $n^{th}$ polytope in the sequence of composihedra, that is, the $n^{th}$ composihedron $CK(n)$.
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机译：我们描述了一个新的多面体序列，这些序列表征了$ A _ { infty} $-图从拓扑半体动物到$ A _ { infty} $-空间。因此，这些多表位中的每一个都是相应的多面体的商。正如先前在拓扑和分类文献中所假设的那样，我们的多聚体序列被证明与associahedra在组合上并不相同。他们获得了新的集体名称composihedra。我们指出在单半双分类中富集的双分类和拟单分子类理论的公式化过程中，如何使用这些多表位对组合物进行参数化。我们还提出了一种简单的算法，用于确定欧几里得空间中的凸包是composihedra序列中的$ n ^ {th} $多面体的极点，即$ n ^ {th} $ composihedron $ CK（n） $。
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