On the Noteworthy Properties of Tangentials in Cubic Structures

The cubic structure, a captivating geometric structure, finds applications across various areas of geometry through different models. In this paper, we explore the significant characteristics of tangentials in cubic structures of ranks 0, 1, and 2. Specifically, in the cubic structure of rank 2, we derive the Hessian configuration (123,164)
of points and lines. Finally, we introduce and investigate the de Vries configuration of points and lines in a cubic structure.