Sensationally non-planar interlocking structures

Автор: Kanel–Belov A.
Сборник: Designing non-traditional materials based on geometrical principles. 19–22 June 2005, Hanover, Germany
Тезисы
Год издания: 2005
Место издания: Abstracts, Workshop in Hanover:
Первая страница: 12
DOI: 10.13140/RG.2.1.5167.5922
Аннотация: In recent works, some interlocking structures were constructed. These structures were based on periodic tailings in a plane and were quasiplanar. In addition, they were unstable in the following sense. After removing a finite set of elements, they can de disassembled one by one. Here we present spatial structures that are interlocking in several planes simultaneously. There is also another spatial effect. If a plane is divided into convex figures, there always one such that it has common edges with no more then 6 its neighbours. However, in 3D space it is not so. For any n there is a division of space into congruent convex bodies such that any one of them has a common face with more than n its neighbours. This construction allows us to have interlocking in any number of layers. In addition, we discuss a way to generate interlocking structures and their possible properties. Finally, we present a review of different interlocking structures and formulate some open problems.
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