We present a computationally efficient algorithm that is suitable for graphic processing unit implementation. This algorithm enables the identification of all weak pseudo-manifolds that meet specific facet conditions, drawn from a given input set. We employ this approach to enumerate toric colorable seeds. Consequently, we achieve a comprehensive characterization of $(n-1)$-dimensional PL spheres with $n+4$ vertices that possess a maximal Buchstaber number. A primary focus of this research is the fundamental categorization of non-singular complete toric varieties of Picard number $4$. This classification serves as a valuable tool for addressing questions related to toric manifolds of Picard number $4$. Notably, we have determined which of these manifolds satisfy equality within an inequality regarding the number of minimal components in their rational curve space. This addresses a question posed by Chen, Fu, and Hwang in 2014 for this specific case.

翻译：我们提出了一种计算高效的算法，适用于图形处理单元的实现。该算法能够从给定输入集合中识别所有满足特定面条件的弱伪流形。我们利用此方法枚举环面可着色种子。由此，我们实现了对具有最大Buchstaber数的$(n-1)$维PL球面（具有$n+4$个顶点）的全面刻画。本研究的一个核心焦点是Picard数为$4$的非奇异完全环面簇的基本分类。这一分类为解决与Picard数为$4$的环面流形相关的问题提供了有价值的工具。值得注意的是，我们确定了这些流形中哪些在其有理曲线空间的最小分支数量不等式上取等。这回答了Chen、Fu和Hwang在2014年针对该特定情形提出的问题。