A simplex is a fundamental geometric shape in mathematics that generalizes the concept of a triangle or tetrahedron to higher dimensions. In two dimensions, a simplex is a triangle, while in three dimensions, it is a tetrahedron. More generally, an n-simplex is defined as the convex hull of its n + 1 vertices, which are not all contained in a single hyperplane. Simplexes are important in various fields, including topology, algebraic geometry, and computational geometry. They serve as building blocks for more complex shapes and structures, allowing mathematicians to study properties of spaces and functions in a systematic way.