Bipyramid

Bipyramid

A bipyramid is a type of polyhedron formed by joining two identical pyramids base-to-base. The resulting shape has a central axis of symmetry and is characterized by its polygonal base and two congruent sets of triangular faces.

Types of Bipyramids

Bipyramids can be classified based on the shape of their base:

• Triangular Bipyramid: Formed by joining two tetrahedra at their bases, resulting in a polyhedron with six triangular faces.
• Square Bipyramid: Created by joining two square pyramids at their bases, resulting in a polyhedron with eight triangular faces.
• Pentagonal Bipyramid: Formed by joining two pentagonal pyramids at their bases, resulting in a polyhedron with ten triangular faces.

Properties

Bipyramids have several notable properties:

• Faces: All faces of a bipyramid are triangular.
• Vertices: The number of vertices is equal to the number of vertices of the base polygon plus two.
• Edges: The number of edges is twice the number of edges of the base polygon.
• Symmetry: Bipyramids have a central axis of symmetry passing through the apexes of the two pyramids.

Applications

Bipyramids are used in various fields such as crystallography, where they describe the shapes of certain crystals. They are also found in geometry and architecture.

Related Polyhedra

Bipyramids are closely related to other polyhedra, including:

• Pyramids
• Prisms
• Antiprisms

See Also

• Polyhedron
• Pyramid (geometry)
• Prism (geometry)
• Antiprism