Английская Википедия:Gyroelongated square cupola

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Шаблон:Infobox polyhedron

Файл:Yitcupola.jpg
An unfolded gyroelongated square cupola
Файл:Johnson solid 23 net.png
An unfolded gyroelongated square cupola, faces colored by symmetry

In geometry, the gyroelongated square cupola is one of the Johnson solids (J23). As the name suggests, it can be constructed by gyroelongating a square cupola (J4) by attaching an octagonal antiprism to its base. It can also be seen as a gyroelongated square bicupola (J45) with one square bicupola removed.

Шаблон:Johnson solid

Area and Volume

The surface area is,

<math>A=\left(7+2\sqrt{2}+5\sqrt{3}\right)a^2\approx 18.4886811...a^2.</math>

The volume is the sum of the volume of a square cupola and the volume of an octagonal prism,

<math>V=\left(1+\frac{2}{3}\sqrt{2} + \frac{2}{3}\sqrt{4+2\sqrt{2}+2\sqrt{146+103\sqrt{2}}}\right)a^3\approx6.2107658...a^3.</math>

Dual polyhedron

The dual of the gyroelongated square cupola has 20 faces: 8 kites, 4 rhombi, and 8 pentagons.

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

External links

Шаблон:Polyhedron-stub Шаблон:Johnson solids navigator