Пятискатная прямая куполоротонда

Пятискатная прямая куполоротонда
(3D-модель)
(3D-модель)
Тип многогранник Джонсона
Свойства выпуклая
Комбинаторика
Элементы
27 граней
50 рёбер
25 вершин 		Χ = 2
Грани 15 треугольников
5 квадратов
7 пятиугольников
Конфигурация вершины 10(3.4.3.5)
5(3.4.5.4)
2x5(3.5.3.5)
Развёртка
Классификация
Обозначения J32, М6+М9
Группа симметрии C5v

Пятиска́тная пряма́я куполорото́нда[1] — один из многогранников Джонсона (J32, по Залгаллеру — М6+М9).

Составлена из 27 граней: 15 правильных треугольников, 5 квадратов и 7 правильных пятиугольников. Среди пятиугольных граней 1 окружена пятью квадратными, остальные 6 — пятью треугольными; каждая квадратная грань окружена пятиугольной и тремя треугольными; среди треугольных граней 5 окружены тремя пятиугольными, 5 — двумя пятиугольными и квадратной, 5 — пятиугольной и двумя квадратными.

Имеет 50 рёбер одинаковой длины. 5 рёбер располагаются между пятиугольной и квадратной гранями, 30 рёбер — между пятиугольной и треугольной, остальные 15 — между квадратной и треугольной.

У пятискатной прямой куполоротонды 25 вершин. В 10 вершинах сходятся две пятиугольных и две треугольных грани; в 5 вершинах — пятиугольная, две квадратных и треугольная; в остальных 10 — пятиугольная, квадратная и две треугольных.

Пятискатную прямую куполоротонду можно получить из двух других многогранников Джонсона — пятискатного купола (J5) и пятискатной ротонды (J6), — приложив их друг к другу десятиугольными гранями так, чтобы параллельные десятиугольным пятиугольные грани двух многогранников оказались повёрнуты одинаково.

Метрические характеристики

Если пятискатная прямая куполоротонда имеет ребро длины , её площадь поверхности и объём выражаются как

Примечания

  1. ↑ Залгаллер В. А. Выпуклые многогранники с правильными гранями / Зап. научн. сем. ЛОМИ, 1967. — Т. 2. — Cтр. 21.

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