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math.MG2023
Covering the Crosspolytope with Crosspolytopes
Antal Joós
Let be the smallest positive number such that the convex body can be covered by translates of . Let be the -dimensional crosspolytope. It will b…
math.MG2022★ 1 cited
Isoperimetric problems for zonotopes
Antal Joós, Zsolt Lángi
Shephard (Canad. J. Math. 26: 302-321, 1974) proved a decomposition theorem for zonotopes yielding a simple formula for their volume. In this note we prove a generalization of this…
math.MG2021
Cubes and Boxes have Rupert's passages in every direction
András Bezdek, Zhenyue Guan, Mihály Hujter +1
It is a year old counterintuitive observation of Prince Rupert of Rhine that in cube a straight tunnel can be cut, through which a second congruent cube can be passed. Hundre…