Covering a Regular Tetrahedron with Diminished Copies
Fangyu Zhang, Yuqin Zhang, Mei Han
Journal of Advances in Mathematics and Computer Science · pp. 23–29 · Published 29 Apr 2021
10.9734/jamcs/2021/v36i430354Abstract
Let T be a unit regular tetrahedron. A diminished copy of T is the image of T under a homothety with positive ratio smaller than 1. Let m be a positive integer and let γm(T) be the smallest positive number r such that T can be covered by m translates of rT. Zong gave the results of γ4(T) = 3/4and γ5(T) = 9/13. However, the values of γ6(T) , γ7(T) and γ8(T) were not given then. In this article we give the upper bounds of γ6(T), γ7(T) and γ8(T).
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