We present a computationally efficient algorithm that is suitable for GPU 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 seed PL-spheres. Consequently, we achieve a comprehensive characterization of PL-spheres of dimension n-1 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 with a Picard number of 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-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GPU实现。该算法能够从给定输入集中识别所有满足特定面条件的弱伪流形。我们采用此方法枚举了toric可着色的种子PL球面。由此，我们实现了对具有最大Buchstaber数的n-1维（含n+4个顶点）PL球面的完整刻画。本研究的一个核心重点是对Picard数为4的非奇异完全toric簇进行基础分类。这一分类为解答与Picard数为4的toric流形相关问题提供了有效工具。值得注意的是，我们确定了这些流形中哪些能在其有理曲线空间的最小分量数量的不等式关系中取等。这回答了Chen-Fu-Hwang在2014年针对该特定情形提出的问题。