This paper introduces an inductive tree notation for all the faces of polytopes arising from a simplex by truncations, which allows viewing face inclusion as the process of contracting tree edges. These polytopes, known as hypergraph polytopes or nestohedra, fit in the interval from simplices to permutohedra (in any finite dimension). This interval was further stretched by Petrić to allow truncations of faces that are themselves obtained by truncations. Our notation applies to all these polytopes. As an illustration, we detail the case of Petrić’s permutohedron-based associahedra. As an application, we present a criterion for determining whether edges of polytopes associated with the coherences of categorified operads correspond to sequential, or to parallel associativity.

中文翻译：

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超图多义词的句法方面

本文针对通过截断的单纯形生成的多边形的所有面引入了归纳树符号，从而可以将面包含视为收缩树边缘的过程。这些多面体，称为超图多面体或巢面，适合于从单纯形到变角体的间隔（任何有限尺寸）。Petrić进一步延长了此间隔，以允许截断本身通过截断获得的脸部。我们的表示法适用于所有这些多表位。作为说明，我们详细介绍了以Petrić的基于高六面体的associahedra的情况。作为一种应用，我们提出了一个标准，用于确定与分类操作符的相干性关联的多边形的边是对应于顺序关联性还是平行关联性。