Tetrahedral and pentahedral cages for discs

Liping Yuan, Tudor Zamfirescu


This paper is about cages for compact convex sets. A cage is the 1-skeleton of a convex polytope in ℝ3. A cage is said to hold a set if the set cannot be continuously moved to a distant location, remaining congruent to itself and disjoint from the cage.

In how many “truly different” positions can (compact 2-dimensional) discs be held by a cage? We completely answer this question for all tetrahedra. Moreover, we present pentahedral cages holding discs in a large number (57) of positions.


Tetrahedral cages, pentahedral cages, discs

Full Text:


DOI: https://doi.org/10.26493/1855-3974.1560.a43

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications