Elongated triangular bipyramid

Elongated triangular bipyramid
Type	Johnson J13 - J14 - J15
Faces	6 triangles 3 squares
Edges	15
Vertices	8
Vertex configuration	2(33) 6(32.42)
Symmetry group	D3h
Dual polyhedron	Triangular bifrustum
Properties	convex
Net

In geometry, the elongated triangular bipyramid (or dipyramid) is one of the Johnson solids (J₁₄), convex polyhedra whose faces are regular polygons. As the name suggests, it can be constructed by elongating a triangular bipyramid (J₁₂) by inserting a triangular prism between its congruent halves.

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.

Formulae

The following formulae for volume and surface area can be used if all faces are regular, with edge length a:

$V=({\frac {1}{12}}(2{\sqrt {2}}+3{\sqrt {3}}))a^{3}\approx 0.668715...a^{3}$

$A=({\frac {3}{2}}(2+{\sqrt {3}}))a^{2}\approx 5.59808...a^{2}$

Dual polyhedron

The dual of the elongated triangular bipyramid has 8 faces: 6 trapezoidal and 2 triangular.

Dual elongated triangular bipyramid	Net of dual

External links

• Weisstein, Eric W. "Johnson solid". MathWorld.
• Weisstein, Eric W. "Elongated triangular bipyramid". MathWorld.