凸多面体的互锁：朝向破碎固体的几何理论
Interlocking of convex polyhedra: towards a geometric theory of fragmented solids
摘要：
我们目前的结构由相同的凸多面体是几何联锁。这些集合不能通过平移和/或旋转移除单个多面体来分解。允许互锁排列的形状包括所有五个柏拉图立体。联锁标准的基础上的转换的横截面的元素在一个三维重建层从其中间的横截面制定。一个推广到更高的维度也给出了。特别地，描述了四维立方体的互锁层。
英文摘要：
We present structures comprised of identical convex polyhedra which are interlocked geometrically. These sets cannot be disassembled by removing individual polyhedra by translations and/or rotations. The shapes that permit interlocking arrangements include all five platonic solids. Criteria for interlocking based on transformations of the cross-sections of the elements in a 3D reconstruction of a layer from its middle cross-section are formulated. A generalization to higher dimensions is also given. In particular, an interlocking layer of four-dimensional cubes is described.
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