In geometry, the elongated triangular bipyramid (or dipyramid) or triakis triangular prism a polyhedron constructed from a triangular prism by attaching two tetrahedrons to its bases. It is an example of Johnson solid.

Construction

The elongated triangular bipyramid is constructed from a triangular prism by attaching two tetrahedrons onto its bases, a process known as the elongation. These tetrahedrons cover the triangular faces so that the resulting polyhedron has nine faces (six of them are equilateral triangles and three of them are squares), fifteen edges, and eight vertices. A convex polyhedron in which all of the faces are regular polygons is the Johnson solid. The elongated bipyramid is one of them, enumerated as the fourteenth Johnson solid J_{14}.

Properties

The surface area of an elongated triangular bipyramid A is the sum of all polygonal face's area: six equilateral triangles and three squares. The volume of an elongated triangular bipyramid V can be ascertained by slicing it off into two tetrahedrons and a regular triangular prism and then adding their volume. The height of an elongated triangular bipyramid h is the sum of two tetrahedrons and a regular triangular prism' height. Therefore, given the edge length a, its surface area and volume is formulated as: It has the same three-dimensional symmetry group as the triangular prism, the dihedral group of order twelve. The dihedral angle of an elongated triangular bipyramid can be calculated by adding the angle of the tetrahedron and the triangular prism:

Appearances

The nirrosula, an African musical instrument woven out of strips of plant leaves, is made in the form of a series of elongated bipyramids with non-equilateral triangles as the faces of their end caps.