This article is part of a series with the aim of classifying all non-hyperoctahedral categories of two-colored partitions. Those constitute by some Tannaka-Krein type result the representation categories of a specific class of quantum groups. In Part I we introduced a class of parameters which gave rise to many new non-hyperoctahedral categories of partitions. In the present article we show that this class actually contains all possible parameter values of all non-hyperoctahedral categories of partitions. This is an important step towards the classification of all non-hyperoctahedral categories.

中文翻译：

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两色分区的非超八面体类别第二部分：所有可能的参数值

本文是该系列文章的一部分，旨在对所有两种颜色分区的非超八面体类别进行分类。由某些Tannaka-Krein类型构成的那些代表特定量子组类别的表示类别。在第一部分中，我们介绍了一类参数，这些参数产生了许多新的非超八面体分区类别。在本文中，我们证明了该类实际上包含所有非八面体分区类别的所有可能参数值。这是对所有非八面体类别进行分类的重要一步。