Abstract
In this paper, we introduce the concept of inflection triplets of points within a cubic structure, explore their fundamental properties, and investigate the relationships between inflection triplets and other key elements of the cubic structure. Special attention is devoted to their relationships with known geometric objects in cubic structures, such as conics. We define conics with triple points and explore their properties and their number. The conics with quadruple points are introduced, and their number is considered. The presented results offer new insights into the interplay between geometric concepts and algebraic frameworks, thereby contributing to a more comprehensive understanding of properties of the cubic structure.