Tetrahedral cages for unit discs
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Liping Yuan
,
Tudor Zamfirescu
Abstract
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 positions can (compact 2-dimensional) unit discs be held by a tetrahedral cage? We completely answer this question for all tetrahedra.
Communicated by: E. Bannai
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Funding: The authors gratefully acknowledge financial support by NSF of China (11871192, 11471095) and the Program for Foreign experts of Hebei Province (No. 2019YX002A, 2020). The research of the second author was also partly supported by the GDRI ECO-Math.
References
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Articles in the same Issue
- Frontmatter
- On vector bundles over reducible curves with a node
- Inscribed rectangle coincidences
- 𝔽p2-maximal curves with many automorphisms are Galois-covered by the Hermitian curve
- Tetrahedral cages for unit discs
- When is M0,n(ℙ1,1) a Mori dream space?
- Rank-one isometries of CAT(0) cube complexes and their centralisers
- Wall-crossing in genus-zero hybrid theory
- The curve Yn = Xℓ(Xm + 1) over finite fields II
- Uniqueness results for bodies of constant width in the hyperbolic plane
- A note on large Kakeya sets
- On static manifolds and related critical spaces with cyclic parallel Ricci tensor
- The motivic Igusa zeta function of a space monomial curve with a plane semigroup
- Real hypersurfaces of non-flat complex space forms with two generalized conditions on the Jacobi structure operator
