Английская Википедия:Elongated triangular cupola

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Шаблон:Short description Шаблон:Infobox polyhedron

In geometry, the elongated triangular cupola is one of the Johnson solids (Шаблон:Math). As the name suggests, it can be constructed by elongating a triangular cupola (Шаблон:Math) by attaching a hexagonal prism to its base.

Шаблон:Johnson solid

Formulae

The following formulae for volume and surface area can be used if all faces are regular, with edge length a:[1]

<math>V=\left(\frac{1}{6}\left(5\sqrt{2}+9\sqrt{3}\right)\right)a^3\approx3.77659...a^3</math>
<math>A=\left(9+\frac{5\sqrt{3}}{2}\right)a^2\approx13.3301...a^2</math>

Dual polyhedron

The dual of the elongated triangular cupola has 15 faces: 6 isosceles triangles, 3 rhombi, and 6 quadrilaterals.

Dual elongated triangular cupola Net of dual
Файл:Dual elongated triangular cupola.png Файл:Dual elongated triangular cupola net.png

Related polyhedra and honeycombs

The elongated triangular cupola can form a tessellation of space with tetrahedra and square pyramids.[2]

References

Шаблон:Reflist

External links

Шаблон:Johnson solids navigator Шаблон:Polyhedron-stub