Geodesic
Tetrahedral and pentahedral cages for discs
Ars Mathematica Contemporanea, Tome 17 (2019) no. 1, pp. 255-270.

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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.
DOI : 10.26493/1855-3974.1560.a43
Keywords: Tetrahedral cages, pentahedral cages, discs 
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Liping Yuan; Tudor Zamfirescu. Tetrahedral and pentahedral cages for discs. Ars Mathematica Contemporanea, Tome 17 (2019) no. 1, pp. 255-270. doi : 10.26493/1855-3974.1560.a43. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.1560.a43/

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