Английская Википедия:Elongated pentagonal pyramid

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Файл:J9 elongated pentagonal pyramid.stl

3D model of an elongated pentagonal pyramid

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

Formulae

The following formulae for the height (<math>H</math>), surface area (<math>A</math>) and volume (<math>V</math>) can be used if all faces are regular, with edge length <math>L</math>:

<math>H = L\cdot \left( 1 + \sqrt{\frac{5 - \sqrt{5}}{10}}\right) \approx L\cdot 1.525731112</math>

<math>A = L^2 \cdot \frac{20 + 5\sqrt{3} + \sqrt{25 + 10\sqrt{5}}}{4} \approx L^2\cdot 8.88554091</math>

<math>V = L^3 \cdot \left( \frac{5 + \sqrt{5} + 6\sqrt{25 + 10\sqrt{5}}}{24} \right) \approx L^3\cdot 2.021980233</math>

Dual polyhedron

The dual of the elongated pentagonal pyramid has 11 faces: 5 triangular, 1 pentagonal and 5 trapezoidal. It is topologically identical to the Johnson solid.

Dual elongated pentagonal pyramid	Net of dual
Файл:Dual elongated pentagonal pyramid.png	Файл:Dual elongated pentagonal pyramid net.png

See also

• Elongated pentagonal bipyramid

External links

• Шаблон:Mathworld2

Шаблон:Polyhedron-stub