Холиэдр

Холиэдр (от англ. holyhedron) — многогранник в трёхмерном пространстве, имеющий в каждой своей грани хотя бы одну дыру, граница которой не имеет общих точек с границей самой грани и границами других дыр в ней.[1]

Идея описанного многогранника принадлежит Джону Конвею, обнародовавшему её в 1990-х годах[2]. Название, являющееся игрой с английскими словами "polyhedron" (многогранник), "holy" (святой) и "hole" (дыра), было предложено Дэвидом Вильсоном в 1997 году. За нахождение примера холиэдра Конвей предлагал приз размером 10,000 USD, делённых на количество граней в примере.[3] Формулировка проблемы Конвея была следующей:

Существует ли многогранник в трёхмерном евклидовом пространстве, имеющий конечное количество граней, каждая из которых является плоской и связной и имеет не односвязную относительную внутренность.

Оригинальный текст (англ.)
Is there a polyhedron in Euclidean three-dimensional space that has only finitely many plane faces, each of which is a closed connected subset of the appropriate plane whose relative interior in that plane is multiply connected?

Первый пример холиэдра, содержащий 78585627 граней, был приведён в 1999 году П. Винсоном.[4][5] В 2003 году Дон Хэтч представил пример холиэдра из всего лишь 492 граней и получил приз в размере 20.33 USD.[1]

Примечания

  1. ↑ 1 2 Weisstein, Eric W. Holyhedron (англ.) на сайте Wolfram MathWorld.
  2. ↑ Статья в книге "Великая математика" Клиффорда Пиковера. Дата обращения: 27 апреля 2020. Архивировано 19 сентября 2019 года.
  3. ↑ Demaine, Erik D.; O'Rourke, Joseph. Computational geometry column 37 // ACM SIGACT News. — 1999. — Сентябрь (т. 30, № 3). — С. 39—42. — doi:10.1145/333623.333625.
  4. ↑ Peterson, Ivars (2002-12-11). "Punctured Polyhedra". Science News. Архивировано 4 марта 2016.
  5. ↑ Vinson, J. On holyhedra (англ.) // Discrete & Computational Geometry[англ.] : journal. — 2000. — Vol. 24, no. 1. — P. 85—104. — doi:10.1007/s004540010033.

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