Английская Википедия:Elongated square cupola

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Шаблон:Short description Шаблон:Infobox polyhedron

In geometry, the elongated square cupola is one of the Johnson solids (Шаблон:Math). As the name suggests, it can be constructed by elongating a square cupola (Шаблон:Math) by attaching an octagonal prism to its base. The solid can be seen as a rhombicuboctahedron with its "lid" (another square cupola) removed.

Шаблон:Johnson solid

Formulae

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

<math>V=\left(3+\frac{8\sqrt{2}}{3}\right)a^3\approx6.77124...a^3</math>
<math>A=\left(15+2\sqrt{2}+\sqrt{3}\right)a^2\approx19.5605...a^2</math>
<math>C=\left(\frac{1}{2}\sqrt{5+2\sqrt{2}}\right)a\approx1.39897...a</math>

Dual polyhedron

The dual of the elongated square cupola has 20 faces: 8 isosceles triangles, 4 kites, 8 quadrilaterals.

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

Related polyhedra and honeycombs

The elongated square cupola forms space-filling honeycombs with tetrahedra and cubes; with cubes and cuboctahedra; and with tetrahedra, elongated square pyramids, and elongated square bipyramids. (The latter two units can be decomposed into cubes and square pyramids.)[2]

References

Шаблон:Reflist

External links

Шаблон:Johnson solids navigator Шаблон:Polyhedron-stub