Английская Википедия:Elongated triangular bipyramid

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Файл:3D Johnson J14.stl

Elongated triangular bipyramid (Шаблон:Math)

In geometry, the elongated triangular bipyramid (or dipyramid) or triakis triangular prism is one of the Johnson solids (Шаблон:Math), convex polyhedra whose faces are regular polygons. As the name suggests, it can be constructed by elongating a triangular bipyramid (Шаблон:Math) 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 (<math>V</math>), surface area (<math>A</math>) and height (<math>H</math>) can be used if all faces are regular, with edge length a:

<math>V=\left(\frac{1}{12}\left(2\sqrt{2}+3\sqrt{3}\right)\right)\cdot a^3\approx 0.668715...a^3</math>

<math>A=\left(\frac{3}{2}\left(2+\sqrt{3}\right)\right)\cdot a^2\approx 5.59808...a^2</math>

<math>H = \frac{3 + 2\sqrt{6}}{3}\cdot a \approx \cdot 2.63299...a</math>

Dual polyhedron

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

Dual elongated triangular bipyramid	Net of dual
Файл:Dual elongated triangular dipyramid.png	Файл:Dual elongated triangular dipyramid net.png

External links

• Шаблон:Mathworld2