simplices

A simplex is a geometric shape that generalizes points, lines, triangles, and their higher-dimensional counterparts. In simple terms, a 0-simplex is a point, a 1-simplex is a line segment connecting two points, a 2-simplex is a triangle formed by three points, and a 3-simplex is a tetrahedron with four points. Higher-dimensional simplices extend this pattern, representing complex shapes with multiple vertices connected in specific ways. They are foundational in fields like topology and geometry, helping to understand and analyze the shape and structure of spaces across various dimensions.