Английская Википедия:Elongated pentagonal gyrocupolarotunda

Материал из Онлайн справочника
Перейти к навигацииПерейти к поиску

Шаблон:Short description Шаблон:Infobox polyhedron

In geometry, the elongated pentagonal gyrocupolarotunda is one of the Johnson solids (Шаблон:Math). As the name suggests, it can be constructed by elongating a pentagonal gyrocupolarotunda (Шаблон:Math) by inserting a decagonal prism between its halves. Rotating either the pentagonal cupola (Шаблон:Math) or the pentagonal rotunda (Шаблон:Math) through 36 degrees before inserting the prism yields an elongated pentagonal orthocupolarotunda (Шаблон:Math).

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=\frac{5}{12}\left(11+5\sqrt{5}+6\sqrt{5+2\sqrt{5}}\right)a^3\approx16.936...a^3</math>
<math>A=\frac{1}{4}\left(60+\sqrt{10\left(190+49\sqrt{5}+21\sqrt{75+30\sqrt{5}}\right)}\right)a^2\approx33.5385...a^2</math>

References

Шаблон:Reflist

External links

Шаблон:Johnson solids navigator Шаблон:Polyhedron-stub