Английская Википедия:Elongated square cupola
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.
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
External links
Шаблон:Johnson solids navigator Шаблон:Polyhedron-stub
- ↑ Stephen Wolfram, "Elongated square cupola" from Wolfram Alpha. Retrieved July 22, 2010.
- ↑ Шаблон:Cite web
