bipiramida

A bipyramid is a polyhedron formed by joining two identical pyramids at their bases. This structure consists of two apex vertices connected by a shared polygonal base, resulting in a three-dimensional shape with a total of *n* + 2 vertices, where *n* is the number of vertices in the base polygon. The simplest bipyramid is the triangular bipyramid, which has five vertices and eight triangular faces, resembling a slightly flattened octahedron.

Bipyramids can be classified based on the type of polygon forming their base. For example, a square bipyramid features a square base with two apex vertices, creating eight triangular faces and six vertices. Similarly, a pentagonal bipyramid has a pentagonal base with ten triangular faces and seven vertices. These shapes are part of the broader category of Catalan solids when their dual forms are considered, though bipyramids themselves are not typically dual to Platonic solids.

In geometry, bipyramids are useful in crystallography and molecular chemistry, where they describe certain molecular structures, such as those found in some boron hydrides or coordination complexes. They also appear in architectural and structural design, where their symmetrical properties can provide stability and aesthetic appeal. The term "bipyramid" originates from the combination of "bi-" (meaning two) and "pyramid," reflecting its construction from two pyramids.

Mathematically, bipyramids can be analyzed using Euler’s formula for polyhedra, which relates the number of vertices (*V*), edges (*E*), and faces (*F*) as *V* – *E* + *F* = 2. For a bipyramid with an *n*-sided base, this yields consistent results, reinforcing their role as valid polyhedra in geometric studies.