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Steffen’s flexible polyhedron is embedded. A proof via symbolic computations Научная публикация

Журнал

Journal for Geometry and Graphics
ISSN: 1433-8157

Вых. Данные

Год: 2025, Том: 29, Номер: 1, Страницы: 79--88 Страниц : 10

Ключевые слова

Euclidean space, flexible polyhedron, embedded polyhedron, symbolic computations

Авторы

Alexandrov V. ^1,2 , Volokitin E. ^1,2

Организации

1	Sobolev Institute of Mathematics
2	Novosibirsk State University

Информация о финансировании (1)

Министерство науки и высшего образования РФ

FWNF-2026-0026

A polyhedron is flexible if it can be continuously deformed preserving the shape and dimensions of each face. In the late 1970's Klaus Steffen constructed a sphere-homeomorphic embedded flexible polyhedron with triangular faces and with 9 vertices only, which is well-known in the theory of flexible polyhedra. At about the same time, a hypothesis was formulated that the Steffen polyhedron has the least possible number of vertices among all embedded flexible polyhedra without boundary. A counterexample to this hypothesis was constructed by Matteo Gallet, Georg Grasegger, Jan Legersky, and Josef Schicho in 2024 only. Surprisingly, until now, no proof has been published in the mathematical literature that the Steffen polyhedron is embedded. Probably, this fact was considered obvious to everyone who made a cardboard model of this polyhedron. In this article, we prove this fact using computer symbolic calculations.

Alexandrov V. , Volokitin E.
Steffen’s flexible polyhedron is embedded. A proof via symbolic computations
Journal for Geometry and Graphics. 2025. V.29. N1. P.79--88.

Поступила в редакцию:	13 авг. 2025 г.
Принята к публикации:	27 авг. 2025 г.
Опубликована в печати:	12 сент. 2025 г.
Опубликована online:	12 сент. 2025 г.

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